LMFDB - Space of modular forms of level 2541, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 44 $
Sturm bound:			$704$
Trace bound:			$7$
Distinguishing $T_p$:			$2$, $5$, $13$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(2541))$.

	Total	New	Old
Modular forms	376	108	268
Cusp forms	329	108	221
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$3$	$7$	$11$	Fricke	Dim.
$+$	$+$	$+$	$+$	$12$
$+$	$+$	$-$	$-$	$15$
$+$	$-$	$+$	$-$	$12$
$+$	$-$	$-$	$+$	$15$
$-$	$+$	$+$	$-$	$16$
$-$	$+$	$-$	$+$	$10$
$-$	$-$	$+$	$+$	$8$
$-$	$-$	$-$	$-$	$20$
Plus space			$+$	$45$
Minus space			$-$	$63$

Trace form

$ 108 q + 104 q^{4} - 8 q^{5} - 4 q^{6} + 2 q^{7} + 108 q^{9} + O(q^{10}) $

$ 108 q + 104 q^{4} - 8 q^{5} - 4 q^{6} + 2 q^{7} + 108 q^{9} + 8 q^{12} + 2 q^{14} + 104 q^{16} - 16 q^{17} - 8 q^{19} + 2 q^{21} + 8 q^{23} - 12 q^{24} + 92 q^{25} + 16 q^{26} + 6 q^{28} - 16 q^{29} + 16 q^{30} + 16 q^{31} + 40 q^{32} + 8 q^{34} - 4 q^{35} + 104 q^{36} + 48 q^{38} + 16 q^{39} + 48 q^{40} - 32 q^{41} - 2 q^{42} + 24 q^{43} - 8 q^{45} + 32 q^{46} + 32 q^{47} + 32 q^{48} + 108 q^{49} + 64 q^{50} + 56 q^{52} - 4 q^{54} + 18 q^{56} + 16 q^{57} + 64 q^{58} + 8 q^{59} + 16 q^{60} - 24 q^{61} + 16 q^{62} + 2 q^{63} + 96 q^{64} - 40 q^{65} + 16 q^{67} - 32 q^{68} - 16 q^{69} + 12 q^{70} - 32 q^{73} - 48 q^{74} + 16 q^{75} + 24 q^{78} + 32 q^{80} + 108 q^{81} + 56 q^{82} + 16 q^{83} + 6 q^{84} - 8 q^{85} + 32 q^{86} + 8 q^{87} - 24 q^{89} - 12 q^{91} + 56 q^{92} + 8 q^{93} - 24 q^{94} + 24 q^{95} - 28 q^{96} - 8 q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(2541))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	11	$q$-expansion
2541.2.a.a	$1$	$20.290$	$\Q$	None	$-2$	$-1$	$-3$	$1$	$+$	$-$	$-$	$q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots$
2541.2.a.b	$1$	$20.290$	$\Q$	None	$-2$	$-1$	$1$	$-1$	$+$	$+$	$-$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
2541.2.a.c	$1$	$20.290$	$\Q$	None	$-1$	$-1$	$-3$	$-1$	$+$	$+$	$-$	$q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
2541.2.a.d	$1$	$20.290$	$\Q$	None	$-1$	$-1$	$1$	$1$	$+$	$-$	$-$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
2541.2.a.e	$1$	$20.290$	$\Q$	None	$0$	$1$	$-3$	$-1$	$-$	$+$	$-$	$q+q^{3}-2q^{4}-3q^{5}-q^{7}+q^{9}-2q^{12}+\cdots$
2541.2.a.f	$1$	$20.290$	$\Q$	None	$0$	$1$	$-3$	$1$	$-$	$-$	$-$	$q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-2q^{12}+\cdots$
2541.2.a.g	$1$	$20.290$	$\Q$	None	$1$	$-1$	$-3$	$1$	$+$	$-$	$-$	$q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
2541.2.a.h	$1$	$20.290$	$\Q$	None	$1$	$-1$	$-2$	$-1$	$+$	$+$	$-$	$q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
2541.2.a.i	$1$	$20.290$	$\Q$	None	$1$	$-1$	$1$	$-1$	$+$	$+$	$-$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2541.2.a.j	$1$	$20.290$	$\Q$	None	$1$	$1$	$-2$	$1$	$-$	$-$	$-$	$q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
2541.2.a.k	$1$	$20.290$	$\Q$	None	$2$	$-1$	$-3$	$-1$	$+$	$+$	$-$	$q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots$
2541.2.a.l	$1$	$20.290$	$\Q$	None	$2$	$-1$	$1$	$1$	$+$	$-$	$-$	$q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
2541.2.a.m	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-3$	$-2$	$1$	$-2$	$+$	$+$	$-$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+\cdots$
2541.2.a.n	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-2$	$-2$	$1$	$2$	$+$	$-$	$+$	$q-q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}+q^{6}+\cdots$
2541.2.a.o	$2$	$20.290$	$\Q(\sqrt{3}) $	None	$-2$	$-2$	$-4$	$2$	$+$	$-$	$-$	$q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
2541.2.a.p	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$-2$	$-1$	$-2$	$+$	$+$	$+$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
2541.2.a.q	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$-2$	$0$	$-2$	$+$	$+$	$+$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
2541.2.a.r	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$2$	$-4$	$2$	$-$	$-$	$+$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
2541.2.a.s	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$2$	$-3$	$-2$	$-$	$+$	$-$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
2541.2.a.t	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$2$	$2$	$-2$	$-$	$+$	$-$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2541.2.a.u	$2$	$20.290$	$\Q(\sqrt{17}) $	None	$-1$	$2$	$2$	$-2$	$-$	$+$	$-$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2541.2.a.v	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$1$	$-2$	$+$	$+$	$-$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots$
2541.2.a.w	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$1$	$2$	$+$	$-$	$+$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
2541.2.a.x	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$-2$	$-1$	$2$	$+$	$-$	$-$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
2541.2.a.y	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$-2$	$0$	$2$	$+$	$-$	$+$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
2541.2.a.z	$2$	$20.290$	$\Q(\sqrt{21}) $	None	$1$	$-2$	$6$	$-2$	$+$	$+$	$-$	$q+\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}-\beta q^{6}+\cdots$
2541.2.a.ba	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$2$	$-4$	$-2$	$-$	$+$	$+$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
2541.2.a.bb	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$2$	$-3$	$2$	$-$	$-$	$+$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
2541.2.a.bc	$2$	$20.290$	$\Q(\sqrt{17}) $	None	$1$	$2$	$2$	$2$	$-$	$-$	$-$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
2541.2.a.bd	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$2$	$-2$	$1$	$-2$	$+$	$+$	$-$	$q+q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}-q^{6}+\cdots$
2541.2.a.be	$2$	$20.290$	$\Q(\sqrt{3}) $	None	$2$	$-2$	$-4$	$-2$	$+$	$+$	$-$	$q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
2541.2.a.bf	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$3$	$-2$	$1$	$2$	$+$	$-$	$+$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
2541.2.a.bg	$3$	$20.290$	3.3.229.1	None	$-2$	$3$	$4$	$3$	$-$	$-$	$-$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots$
2541.2.a.bh	$3$	$20.290$	3.3.316.1	None	$-1$	$3$	$1$	$-3$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bi	$3$	$20.290$	3.3.837.1	None	$0$	$-3$	$0$	$3$	$+$	$-$	$-$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bj	$3$	$20.290$	3.3.316.1	None	$1$	$3$	$1$	$3$	$-$	$-$	$-$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bk	$4$	$20.290$	4.4.7488.1	None	$-2$	$-4$	$6$	$-4$	$+$	$+$	$+$	$q+\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
2541.2.a.bl	$4$	$20.290$	4.4.7488.1	None	$-2$	$4$	$-2$	$4$	$-$	$-$	$+$	$q+\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
2541.2.a.bm	$4$	$20.290$	4.4.725.1	None	$-1$	$-4$	$-4$	$4$	$+$	$-$	$-$	$q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots$
2541.2.a.bn	$4$	$20.290$	4.4.725.1	None	$1$	$-4$	$-4$	$-4$	$+$	$+$	$+$	$q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots$
2541.2.a.bo	$4$	$20.290$	4.4.7488.1	None	$2$	$-4$	$6$	$4$	$+$	$-$	$+$	$q-\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
2541.2.a.bp	$4$	$20.290$	4.4.7488.1	None	$2$	$4$	$-2$	$-4$	$-$	$+$	$+$	$q-\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
2541.2.a.bq	$10$	$20.290$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$10$	$5$	$-10$	$-$	$+$	$+$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
2541.2.a.br	$10$	$20.290$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$10$	$5$	$10$	$-$	$-$	$-$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(2541))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(2541)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(11))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(21))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(33))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(77))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(121))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(231))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(363))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(847))$$^{\oplus 2}$

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Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(704\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(13\)

\(3\)	\(7\)	\(11\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(12\)
\(+\)	\(+\)	\(-\)	\(-\)	\(15\)
\(+\)	\(-\)	\(+\)	\(-\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)	\(15\)
\(-\)	\(+\)	\(+\)	\(-\)	\(16\)
\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(20\)
Plus space			\(+\)	\(45\)
Minus space			\(-\)	\(63\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2541))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	2541.2.a

Level	$2541$
Weight	$2$
Character orbit	2541.a
Rep. character	$\chi_{2541}(1,\cdot)$
Character field	$\Q$
Dimension	$108$
Newform subspaces	$44$
Sturm bound	$704$
Trace bound	$7$

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	11	$q$-expansion
2541.2.a.a	$1$	$20.290$	\(\Q\)	None	\(-2\)	\(-1\)	\(-3\)	\(1\)	$+$	$-$	$-$	\(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
2541.2.a.b	$1$	$20.290$	\(\Q\)	None	\(-2\)	\(-1\)	\(1\)	\(-1\)	$+$	$+$	$-$	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2541.2.a.c	$1$	$20.290$	\(\Q\)	None	\(-1\)	\(-1\)	\(-3\)	\(-1\)	$+$	$+$	$-$	\(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2541.2.a.d	$1$	$20.290$	\(\Q\)	None	\(-1\)	\(-1\)	\(1\)	\(1\)	$+$	$-$	$-$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.e	$1$	$20.290$	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(-1\)	$-$	$+$	$-$	\(q+q^{3}-2q^{4}-3q^{5}-q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.f	$1$	$20.290$	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(1\)	$-$	$-$	$-$	\(q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.g	$1$	$20.290$	\(\Q\)	None	\(1\)	\(-1\)	\(-3\)	\(1\)	$+$	$-$	$-$	\(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
2541.2.a.h	$1$	$20.290$	\(\Q\)	None	\(1\)	\(-1\)	\(-2\)	\(-1\)	$+$	$+$	$-$	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.i	$1$	$20.290$	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(-1\)	$+$	$+$	$-$	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.j	$1$	$20.290$	\(\Q\)	None	\(1\)	\(1\)	\(-2\)	\(1\)	$-$	$-$	$-$	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.k	$1$	$20.290$	\(\Q\)	None	\(2\)	\(-1\)	\(-3\)	\(-1\)	$+$	$+$	$-$	\(q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
2541.2.a.l	$1$	$20.290$	\(\Q\)	None	\(2\)	\(-1\)	\(1\)	\(1\)	$+$	$-$	$-$	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
2541.2.a.m	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(-3\)	\(-2\)	\(1\)	\(-2\)	$+$	$+$	$-$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+\cdots\)
2541.2.a.n	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(-2\)	\(-2\)	\(1\)	\(2\)	$+$	$-$	$+$	\(q-q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}+q^{6}+\cdots\)
2541.2.a.o	$2$	$20.290$	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(-2\)	\(-4\)	\(2\)	$+$	$-$	$-$	\(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.p	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(-2\)	\(-1\)	\(-2\)	$+$	$+$	$+$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.q	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(-2\)	\(0\)	\(-2\)	$+$	$+$	$+$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.r	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(2\)	\(-4\)	\(2\)	$-$	$-$	$+$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.s	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(2\)	\(-3\)	\(-2\)	$-$	$+$	$-$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.t	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(2\)	\(2\)	\(-2\)	$-$	$+$	$-$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.u	$2$	$20.290$	\(\Q(\sqrt{17}) \)	None	\(-1\)	\(2\)	\(2\)	\(-2\)	$-$	$+$	$-$	\(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.v	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(1\)	\(-2\)	$+$	$+$	$-$	\(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
2541.2.a.w	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(1\)	\(2\)	$+$	$-$	$+$	\(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.x	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(1\)	\(-2\)	\(-1\)	\(2\)	$+$	$-$	$-$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.y	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(1\)	\(-2\)	\(0\)	\(2\)	$+$	$-$	$+$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.z	$2$	$20.290$	\(\Q(\sqrt{21}) \)	None	\(1\)	\(-2\)	\(6\)	\(-2\)	$+$	$+$	$-$	\(q+\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}-\beta q^{6}+\cdots\)
2541.2.a.ba	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(1\)	\(2\)	\(-4\)	\(-2\)	$-$	$+$	$+$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.bb	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(1\)	\(2\)	\(-3\)	\(2\)	$-$	$-$	$+$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.bc	$2$	$20.290$	\(\Q(\sqrt{17}) \)	None	\(1\)	\(2\)	\(2\)	\(2\)	$-$	$-$	$-$	\(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
2541.2.a.bd	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(2\)	\(-2\)	\(1\)	\(-2\)	$+$	$+$	$-$	\(q+q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}-q^{6}+\cdots\)
2541.2.a.be	$2$	$20.290$	\(\Q(\sqrt{3}) \)	None	\(2\)	\(-2\)	\(-4\)	\(-2\)	$+$	$+$	$-$	\(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.bf	$2$	$20.290$	\(\Q(\sqrt{5}) \)	None	\(3\)	\(-2\)	\(1\)	\(2\)	$+$	$-$	$+$	\(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.bg	$3$	$20.290$	3.3.229.1	None	\(-2\)	\(3\)	\(4\)	\(3\)	$-$	$-$	$-$	\(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots\)
2541.2.a.bh	$3$	$20.290$	3.3.316.1	None	\(-1\)	\(3\)	\(1\)	\(-3\)	$-$	$+$	$-$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bi	$3$	$20.290$	3.3.837.1	None	\(0\)	\(-3\)	\(0\)	\(3\)	$+$	$-$	$-$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bj	$3$	$20.290$	3.3.316.1	None	\(1\)	\(3\)	\(1\)	\(3\)	$-$	$-$	$-$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bk	$4$	$20.290$	4.4.7488.1	None	\(-2\)	\(-4\)	\(6\)	\(-4\)	$+$	$+$	$+$	\(q+\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bl	$4$	$20.290$	4.4.7488.1	None	\(-2\)	\(4\)	\(-2\)	\(4\)	$-$	$-$	$+$	\(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bm	$4$	$20.290$	4.4.725.1	None	\(-1\)	\(-4\)	\(-4\)	\(4\)	$+$	$-$	$-$	\(q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bn	$4$	$20.290$	4.4.725.1	None	\(1\)	\(-4\)	\(-4\)	\(-4\)	$+$	$+$	$+$	\(q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bo	$4$	$20.290$	4.4.7488.1	None	\(2\)	\(-4\)	\(6\)	\(4\)	$+$	$-$	$+$	\(q-\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bp	$4$	$20.290$	4.4.7488.1	None	\(2\)	\(4\)	\(-2\)	\(-4\)	$-$	$+$	$+$	\(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bq	$10$	$20.290$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(10\)	\(5\)	\(-10\)	$-$	$+$	$+$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
2541.2.a.br	$10$	$20.290$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(10\)	\(5\)	\(10\)	$-$	$-$	$-$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)