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Properties

Label 931.2.p
Level $931$
Weight $2$
Character orbit 931.p
Rep. character $\chi_{931}(293,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $9$
Sturm bound $186$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(186\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(931, [\chi])\).

Total New Old
Modular forms 200 144 56
Cusp forms 168 128 40
Eisenstein series 32 16 16

Trace form

\( 128 q + 6 q^{2} + 66 q^{4} - 58 q^{9} + O(q^{10}) \) \( 128 q + 6 q^{2} + 66 q^{4} - 58 q^{9} + 12 q^{11} - 6 q^{15} - 66 q^{16} + 12 q^{22} + 6 q^{23} + 52 q^{25} - 12 q^{29} + 92 q^{30} - 12 q^{32} + 66 q^{36} - 48 q^{39} - 24 q^{44} + 6 q^{51} - 6 q^{53} + 46 q^{57} - 92 q^{58} - 96 q^{60} - 164 q^{64} - 12 q^{67} + 18 q^{71} + 36 q^{72} + 30 q^{74} - 126 q^{78} - 18 q^{79} + 16 q^{81} + 26 q^{85} + 48 q^{86} + 24 q^{92} - 88 q^{93} - 96 q^{95} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(931, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
931.2.p.a 931.p 133.p $2$ $7.434$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
931.2.p.b 931.p 133.p $2$ $7.434$ \(\Q(\sqrt{-3}) \) None \(-3\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
931.2.p.c 931.p 133.p $2$ $7.434$ \(\Q(\sqrt{-3}) \) None \(3\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
931.2.p.d 931.p 133.p $2$ $7.434$ \(\Q(\sqrt{-3}) \) None \(3\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
931.2.p.e 931.p 133.p $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(3\) \(-1\) \(9\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3})q^{2}+(-1+2\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
931.2.p.f 931.p 133.p $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(3\) \(1\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3})q^{2}+(1-2\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
931.2.p.g 931.p 133.p $16$ $7.434$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-4\) \(9\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{6}-\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)
931.2.p.h 931.p 133.p $16$ $7.434$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(4\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(1-\beta _{6}+\beta _{9})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
931.2.p.i 931.p 133.p $80$ $7.434$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(931, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(931, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)