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.

\(3\)\(7\)\(11\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(+\)\(42\)\(12\)\(30\)\(37\)\(12\)\(25\)\(5\)\(0\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(51\)\(15\)\(36\)\(45\)\(15\)\(30\)\(6\)\(0\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(48\)\(12\)\(36\)\(42\)\(12\)\(30\)\(6\)\(0\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(47\)\(15\)\(32\)\(41\)\(15\)\(26\)\(6\)\(0\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(52\)\(16\)\(36\)\(46\)\(16\)\(30\)\(6\)\(0\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(43\)\(10\)\(33\)\(37\)\(10\)\(27\)\(6\)\(0\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(46\)\(8\)\(38\)\(40\)\(8\)\(32\)\(6\)\(0\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(47\)\(20\)\(27\)\(41\)\(20\)\(21\)\(6\)\(0\)\(6\)
Plus space\(+\)\(178\)\(45\)\(133\)\(155\)\(45\)\(110\)\(23\)\(0\)\(23\)
Minus space\(-\)\(198\)\(63\)\(135\)\(174\)\(63\)\(111\)\(24\)\(0\)\(24\)

Trace form

\( 108 q + 104 q^{4} - 8 q^{5} - 4 q^{6} + 2 q^{7} + 108 q^{9} + 8 q^{12} + 2 q^{14} + 104 q^{16} - 16 q^{17} - 8 q^{19} + 2 q^{21} + 8 q^{23} - 12 q^{24} + 92 q^{25} + 16 q^{26} + 6 q^{28} - 16 q^{29} + 16 q^{30}+ \cdots - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist 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 2541.2.a.a \(-2\) \(-1\) \(-3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
2541.2.a.b 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.b \(-2\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2541.2.a.c 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.c \(-1\) \(-1\) \(-3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2541.2.a.d 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.d \(-1\) \(-1\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.e 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.e \(0\) \(1\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{5}-q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.f 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.e \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.g 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.c \(1\) \(-1\) \(-3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
2541.2.a.h 2541.a 1.a $1$ $20.290$ \(\Q\) None 231.2.a.a \(1\) \(-1\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.i 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.d \(1\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.j 2541.a 1.a $1$ $20.290$ \(\Q\) None 21.2.a.a \(1\) \(1\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.k 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.a \(2\) \(-1\) \(-3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
2541.2.a.l 2541.a 1.a $1$ $20.290$ \(\Q\) None 2541.2.a.b \(2\) \(-1\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
2541.2.a.m 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.a \(-3\) \(-2\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+\cdots\)
2541.2.a.n 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.c \(-2\) \(-2\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}+q^{6}+\cdots\)
2541.2.a.o 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{3}) \) None 2541.2.a.o \(-2\) \(-2\) \(-4\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.p 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.b \(-1\) \(-2\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.q 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 2541.2.a.q \(-1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.r 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 2541.2.a.r \(-1\) \(2\) \(-4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.s 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.d \(-1\) \(2\) \(-3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.t 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.a.c \(-1\) \(2\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.u 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{17}) \) None 2541.2.a.u \(-1\) \(2\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.v 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.e \(0\) \(-2\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
2541.2.a.w 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.e \(0\) \(-2\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.x 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.b \(1\) \(-2\) \(-1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.y 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 2541.2.a.q \(1\) \(-2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.z 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{21}) \) None 231.2.a.b \(1\) \(-2\) \(6\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}-\beta q^{6}+\cdots\)
2541.2.a.ba 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 2541.2.a.r \(1\) \(2\) \(-4\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.bb 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.d \(1\) \(2\) \(-3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.bc 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{17}) \) None 2541.2.a.u \(1\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
2541.2.a.bd 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.c \(2\) \(-2\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}-q^{6}+\cdots\)
2541.2.a.be 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{3}) \) None 2541.2.a.o \(2\) \(-2\) \(-4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.bf 2541.a 1.a $2$ $20.290$ \(\Q(\sqrt{5}) \) None 231.2.j.a \(3\) \(-2\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.bg 2541.a 1.a $3$ $20.290$ 3.3.229.1 None 231.2.a.e \(-2\) \(3\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots\)
2541.2.a.bh 2541.a 1.a $3$ $20.290$ 3.3.316.1 None 2541.2.a.bh \(-1\) \(3\) \(1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bi 2541.a 1.a $3$ $20.290$ 3.3.837.1 None 231.2.a.d \(0\) \(-3\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bj 2541.a 1.a $3$ $20.290$ 3.3.316.1 None 2541.2.a.bh \(1\) \(3\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bk 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None 2541.2.a.bk \(-2\) \(-4\) \(6\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bl 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None 2541.2.a.bl \(-2\) \(4\) \(-2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bm 2541.a 1.a $4$ $20.290$ 4.4.725.1 None 231.2.j.f \(-1\) \(-4\) \(-4\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bn 2541.a 1.a $4$ $20.290$ 4.4.725.1 None 231.2.j.f \(1\) \(-4\) \(-4\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bo 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None 2541.2.a.bk \(2\) \(-4\) \(6\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bp 2541.a 1.a $4$ $20.290$ 4.4.7488.1 None 2541.2.a.bl \(2\) \(4\) \(-2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bq 2541.a 1.a $10$ $20.290$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 231.2.j.g \(0\) \(10\) \(5\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
2541.2.a.br 2541.a 1.a $10$ $20.290$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 231.2.j.g \(0\) \(10\) \(5\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)

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

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