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Properties

Label 7935.2.a
Level $7935$
Weight $2$
Character orbit 7935.a
Rep. character $\chi_{7935}(1,\cdot)$
Character field $\Q$
Dimension $336$
Newform subspaces $49$
Sturm bound $2208$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7935.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 49 \)
Sturm bound: \(2208\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7935))\).

Total New Old
Modular forms 1152 336 816
Cusp forms 1057 336 721
Eisenstein series 95 0 95

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

\(3\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(41\)
\(+\)\(+\)\(-\)$-$\(44\)
\(+\)\(-\)\(+\)$-$\(51\)
\(+\)\(-\)\(-\)$+$\(33\)
\(-\)\(+\)\(+\)$-$\(43\)
\(-\)\(+\)\(-\)$+$\(40\)
\(-\)\(-\)\(+\)$+$\(33\)
\(-\)\(-\)\(-\)$-$\(51\)
Plus space\(+\)\(147\)
Minus space\(-\)\(189\)

Trace form

\( 336 q + 4 q^{2} - 2 q^{3} + 340 q^{4} + 2 q^{6} + 12 q^{8} + 336 q^{9} + O(q^{10}) \) \( 336 q + 4 q^{2} - 2 q^{3} + 340 q^{4} + 2 q^{6} + 12 q^{8} + 336 q^{9} + 4 q^{10} + 16 q^{11} - 6 q^{12} - 8 q^{13} - 8 q^{14} + 2 q^{15} + 340 q^{16} + 4 q^{18} + 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{22} - 6 q^{24} + 336 q^{25} + 24 q^{26} - 2 q^{27} + 8 q^{28} + 16 q^{29} + 2 q^{30} + 16 q^{31} + 28 q^{32} - 24 q^{34} + 8 q^{35} + 340 q^{36} + 16 q^{37} + 8 q^{38} - 4 q^{39} + 12 q^{40} + 24 q^{41} + 8 q^{43} + 24 q^{44} + 16 q^{47} + 2 q^{48} + 328 q^{49} + 4 q^{50} + 12 q^{51} - 32 q^{52} - 8 q^{53} + 2 q^{54} - 32 q^{56} - 16 q^{57} + 24 q^{58} + 6 q^{60} - 16 q^{61} - 32 q^{62} + 348 q^{64} + 16 q^{65} + 16 q^{66} + 8 q^{67} + 24 q^{68} - 24 q^{70} + 24 q^{71} + 12 q^{72} + 8 q^{73} - 2 q^{75} - 40 q^{77} - 28 q^{78} + 8 q^{79} + 336 q^{81} + 32 q^{82} - 8 q^{83} - 8 q^{84} + 8 q^{85} - 20 q^{87} + 16 q^{88} + 8 q^{89} + 4 q^{90} - 32 q^{91} - 16 q^{93} + 24 q^{94} - 30 q^{96} + 44 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7935))\) 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 5 23
7935.2.a.a 7935.a 1.a $1$ $63.361$ \(\Q\) None \(-2\) \(1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{7}+\cdots\)
7935.2.a.b 7935.a 1.a $1$ $63.361$ \(\Q\) None \(-2\) \(1\) \(-1\) \(5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+5q^{7}+\cdots\)
7935.2.a.c 7935.a 1.a $1$ $63.361$ \(\Q\) None \(-2\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
7935.2.a.d 7935.a 1.a $1$ $63.361$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
7935.2.a.e 7935.a 1.a $1$ $63.361$ \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
7935.2.a.f 7935.a 1.a $1$ $63.361$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
7935.2.a.g 7935.a 1.a $1$ $63.361$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
7935.2.a.h 7935.a 1.a $1$ $63.361$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-q^{11}+\cdots\)
7935.2.a.i 7935.a 1.a $1$ $63.361$ \(\Q\) None \(0\) \(1\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+3q^{7}+q^{9}+4q^{11}+\cdots\)
7935.2.a.j 7935.a 1.a $1$ $63.361$ \(\Q\) None \(1\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
7935.2.a.k 7935.a 1.a $1$ $63.361$ \(\Q\) None \(2\) \(-1\) \(-1\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-3q^{7}+\cdots\)
7935.2.a.l 7935.a 1.a $1$ $63.361$ \(\Q\) None \(2\) \(1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
7935.2.a.m 7935.a 1.a $1$ $63.361$ \(\Q\) None \(2\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
7935.2.a.n 7935.a 1.a $2$ $63.361$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots\)
7935.2.a.o 7935.a 1.a $2$ $63.361$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}+(2-2\beta )q^{7}+\cdots\)
7935.2.a.p 7935.a 1.a $2$ $63.361$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{5}-\beta q^{6}+(-2+2\beta )q^{7}+\cdots\)
7935.2.a.q 7935.a 1.a $2$ $63.361$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{5}-\beta q^{6}+(1+2\beta )q^{7}+\cdots\)
7935.2.a.r 7935.a 1.a $2$ $63.361$ \(\Q(\sqrt{73}) \) None \(0\) \(2\) \(-2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-\beta q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7935.2.a.s 7935.a 1.a $2$ $63.361$ \(\Q(\sqrt{73}) \) None \(0\) \(2\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+\beta q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7935.2.a.t 7935.a 1.a $2$ $63.361$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
7935.2.a.u 7935.a 1.a $3$ $63.361$ 3.3.316.1 None \(-1\) \(3\) \(-3\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.v 7935.a 1.a $3$ $63.361$ 3.3.148.1 None \(0\) \(-3\) \(-3\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
7935.2.a.w 7935.a 1.a $3$ $63.361$ 3.3.148.1 None \(0\) \(-3\) \(3\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+\cdots\)
7935.2.a.x 7935.a 1.a $3$ $63.361$ 3.3.756.1 None \(0\) \(-3\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.y 7935.a 1.a $3$ $63.361$ 3.3.756.1 None \(0\) \(-3\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.z 7935.a 1.a $4$ $63.361$ 4.4.25492.1 None \(0\) \(4\) \(-4\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2}+\beta _{3})q^{4}-q^{5}+\cdots\)
7935.2.a.ba 7935.a 1.a $4$ $63.361$ 4.4.25492.1 None \(0\) \(4\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+q^{5}+\cdots\)
7935.2.a.bb 7935.a 1.a $5$ $63.361$ 5.5.3370660.1 None \(0\) \(5\) \(-5\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bc 7935.a 1.a $5$ $63.361$ 5.5.3370660.1 None \(0\) \(5\) \(5\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bd 7935.a 1.a $6$ $63.361$ 6.6.22733568.1 None \(0\) \(-6\) \(-6\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.be 7935.a 1.a $6$ $63.361$ 6.6.22733568.1 None \(0\) \(-6\) \(6\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bf 7935.a 1.a $6$ $63.361$ 6.6.4507648.1 None \(0\) \(6\) \(-6\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
7935.2.a.bg 7935.a 1.a $6$ $63.361$ 6.6.4507648.1 None \(0\) \(6\) \(6\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
7935.2.a.bh 7935.a 1.a $8$ $63.361$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-8\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bi 7935.a 1.a $8$ $63.361$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(8\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bj 7935.a 1.a $10$ $63.361$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-10\) \(-10\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bk 7935.a 1.a $10$ $63.361$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-10\) \(10\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
7935.2.a.bl 7935.a 1.a $12$ $63.361$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(-12\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{7}-\beta _{8})q^{4}-q^{5}+\cdots\)
7935.2.a.bm 7935.a 1.a $12$ $63.361$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(12\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{7}-\beta _{8})q^{4}+q^{5}+\cdots\)
7935.2.a.bn 7935.a 1.a $15$ $63.361$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-8\) \(15\) \(-15\) \(13\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
7935.2.a.bo 7935.a 1.a $15$ $63.361$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-8\) \(15\) \(15\) \(-13\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
7935.2.a.bp 7935.a 1.a $15$ $63.361$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(-15\) \(-15\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{2}-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
7935.2.a.bq 7935.a 1.a $15$ $63.361$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(-15\) \(15\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{2}-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
7935.2.a.br 7935.a 1.a $16$ $63.361$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-16\) \(-16\) \(-12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bs 7935.a 1.a $16$ $63.361$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-16\) \(16\) \(12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
7935.2.a.bt 7935.a 1.a $25$ $63.361$ None \(1\) \(-25\) \(-25\) \(15\) $+$ $+$ $-$ $\mathrm{SU}(2)$
7935.2.a.bu 7935.a 1.a $25$ $63.361$ None \(1\) \(-25\) \(25\) \(-15\) $+$ $-$ $+$ $\mathrm{SU}(2)$
7935.2.a.bv 7935.a 1.a $25$ $63.361$ None \(11\) \(25\) \(-25\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$
7935.2.a.bw 7935.a 1.a $25$ $63.361$ None \(11\) \(25\) \(25\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7935))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7935)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\)\(^{\oplus 2}\)