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Properties

Label 931.4.a
Level $931$
Weight $4$
Character orbit 931.a
Rep. character $\chi_{931}(1,\cdot)$
Character field $\Q$
Dimension $184$
Newform subspaces $15$
Sturm bound $373$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 931.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(373\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(931))\).

Total New Old
Modular forms 288 184 104
Cusp forms 272 184 88
Eisenstein series 16 0 16

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

\(7\)\(19\)FrickeDim
\(+\)\(+\)$+$\(46\)
\(+\)\(-\)$-$\(42\)
\(-\)\(+\)$-$\(45\)
\(-\)\(-\)$+$\(51\)
Plus space\(+\)\(97\)
Minus space\(-\)\(87\)

Trace form

\( 184 q + 4 q^{2} - 4 q^{3} + 722 q^{4} + 30 q^{5} - 10 q^{6} + 12 q^{8} + 1674 q^{9} + O(q^{10}) \) \( 184 q + 4 q^{2} - 4 q^{3} + 722 q^{4} + 30 q^{5} - 10 q^{6} + 12 q^{8} + 1674 q^{9} - 100 q^{10} - 90 q^{11} + 100 q^{12} + 76 q^{13} - 48 q^{15} + 3094 q^{16} + 8 q^{17} + 408 q^{18} + 38 q^{19} + 376 q^{20} + 152 q^{22} - 22 q^{23} - 254 q^{24} + 4874 q^{25} + 50 q^{26} + 344 q^{27} + 168 q^{29} + 1052 q^{30} - 460 q^{31} - 80 q^{32} + 20 q^{33} - 216 q^{34} + 7444 q^{36} - 188 q^{37} + 114 q^{38} + 354 q^{39} + 372 q^{40} + 20 q^{41} - 530 q^{43} - 984 q^{44} - 246 q^{45} + 1076 q^{46} + 1070 q^{47} - 352 q^{48} - 1576 q^{50} - 412 q^{51} + 720 q^{52} - 2180 q^{53} - 674 q^{54} + 1350 q^{55} - 114 q^{57} - 2790 q^{58} + 1420 q^{59} - 3196 q^{60} + 1154 q^{61} - 720 q^{62} + 10814 q^{64} + 396 q^{65} + 444 q^{66} + 2248 q^{67} - 1206 q^{68} - 492 q^{69} - 1816 q^{71} - 1148 q^{72} - 1100 q^{73} + 472 q^{74} - 872 q^{75} + 380 q^{76} + 2432 q^{78} + 1476 q^{79} + 7544 q^{80} + 15552 q^{81} + 2528 q^{82} - 636 q^{83} + 3766 q^{85} - 11892 q^{86} + 3322 q^{87} - 7956 q^{88} - 332 q^{89} - 4556 q^{90} - 5926 q^{92} - 1932 q^{93} - 1500 q^{94} - 1026 q^{95} - 5250 q^{96} + 3540 q^{97} - 7710 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(931))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 19
931.4.a.a 931.a 1.a $1$ $54.931$ \(\Q\) None \(-3\) \(5\) \(12\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+5q^{3}+q^{4}+12q^{5}-15q^{6}+\cdots\)
931.4.a.b 931.a 1.a $1$ $54.931$ \(\Q\) None \(4\) \(-8\) \(-6\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-8q^{3}+8q^{4}-6q^{5}-2^{5}q^{6}+\cdots\)
931.4.a.c 931.a 1.a $3$ $54.931$ 3.3.3144.1 None \(3\) \(-1\) \(-14\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}-2\beta _{2})q^{3}+\cdots\)
931.4.a.d 931.a 1.a $6$ $54.931$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-3\) \(3\) \(13\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
931.4.a.e 931.a 1.a $6$ $54.931$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(3\) \(-7\) \(29\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
931.4.a.f 931.a 1.a $7$ $54.931$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(17\) \(33\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(2-\beta _{3})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
931.4.a.g 931.a 1.a $8$ $54.931$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(-13\) \(-37\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
931.4.a.h 931.a 1.a $14$ $54.931$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(-6\) \(-40\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots\)
931.4.a.i 931.a 1.a $14$ $54.931$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(6\) \(40\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
931.4.a.j 931.a 1.a $16$ $54.931$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-7\) \(0\) \(-15\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
931.4.a.k 931.a 1.a $16$ $54.931$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-7\) \(0\) \(15\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
931.4.a.l 931.a 1.a $20$ $54.931$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(0\) \(-1\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(5+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
931.4.a.m 931.a 1.a $20$ $54.931$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(0\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(5+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
931.4.a.n 931.a 1.a $26$ $54.931$ None \(2\) \(-12\) \(-80\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
931.4.a.o 931.a 1.a $26$ $54.931$ None \(2\) \(12\) \(80\) \(0\) $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(931))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(931)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 2}\)