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Properties

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 $7$

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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.

\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(12\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(12\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(20\)
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 Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 11
2541.2.a.a 2541.a 1.a $1$ $20.290$ \(\Q\) None \(-2\) \(-1\) \(-3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
2541.2.a.b 2541.a 1.a $1$ $20.290$ \(\Q\) None \(-2\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2541.2.a.c 2541.a 1.a $1$ $20.290$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2541.2.a.d 2541.a 1.a $1$ $20.290$ \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.e 2541.a 1.a $1$ $20.290$ \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{5}-q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.f 2541.a 1.a $1$ $20.290$ \(\Q\) None \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.g 2541.a 1.a $1$ $20.290$ \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
2541.2.a.h 2541.a 1.a $1$ $20.290$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.i 2541.a 1.a $1$ $20.290$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.j 2541.a 1.a $1$ $20.290$ \(\Q\) None \(1\) \(1\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.k 2541.a 1.a $1$ $20.290$ \(\Q\) None \(2\) \(-1\) \(-3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
2541.2.a.l 2541.a 1.a $1$ $20.290$ \(\Q\) None \(2\) \(-1\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
2541.2.a.m 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+\cdots\)
2541.2.a.n 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}+q^{6}+\cdots\)
2541.2.a.o 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-4\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.p 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.q 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.r 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(-4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.s 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(-3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.t 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.u 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.v 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
2541.2.a.w 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.x 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.y 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.z 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{21}) \) None \(1\) \(-2\) \(6\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}-\beta q^{6}+\cdots\)
2541.2.a.ba 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(-4\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.bb 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(-3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.bc 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{17}) \) None \(1\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
2541.2.a.bd 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}-q^{6}+\cdots\)
2541.2.a.be 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.bf 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None \(3\) \(-2\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.bg 2541.a 1.a $3$ $20.290$ 3.3.229.1 None \(-2\) \(3\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots\)
2541.2.a.bh 2541.a 1.a $3$ $20.290$ 3.3.316.1 None \(-1\) \(3\) \(1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bi 2541.a 1.a $3$ $20.290$ 3.3.837.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bj 2541.a 1.a $3$ $20.290$ 3.3.316.1 None \(1\) \(3\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bk 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None \(-2\) \(-4\) \(6\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bl 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None \(-2\) \(4\) \(-2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bm 2541.a 1.a $4$ $20.290$ 4.4.725.1 None \(-1\) \(-4\) \(-4\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bn 2541.a 1.a $4$ $20.290$ 4.4.725.1 None \(1\) \(-4\) \(-4\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bo 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None \(2\) \(-4\) \(6\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bp 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None \(2\) \(4\) \(-2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bq 2541.a 1.a $10$ $20.290$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(5\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
2541.2.a.br 2541.a 1.a $10$ $20.290$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(5\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)

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

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