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Properties

Label 946.2.e
Level $946$
Weight $2$
Character orbit 946.e
Rep. character $\chi_{946}(221,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $76$
Newform subspaces $14$
Sturm bound $264$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 946 = 2 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 946.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(264\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(946, [\chi])\).

Total New Old
Modular forms 272 76 196
Cusp forms 256 76 180
Eisenstein series 16 0 16

Trace form

\( 76 q + 76 q^{4} + 4 q^{5} - 4 q^{6} + 8 q^{7} - 46 q^{9} + O(q^{10}) \) \( 76 q + 76 q^{4} + 4 q^{5} - 4 q^{6} + 8 q^{7} - 46 q^{9} - 4 q^{13} + 8 q^{14} + 76 q^{16} - 12 q^{19} + 4 q^{20} + 32 q^{21} - 4 q^{22} - 4 q^{23} - 4 q^{24} - 30 q^{25} + 16 q^{26} + 24 q^{27} + 8 q^{28} - 20 q^{29} - 16 q^{30} + 26 q^{31} + 4 q^{33} + 4 q^{34} - 96 q^{35} - 46 q^{36} + 12 q^{37} - 14 q^{38} + 16 q^{39} - 48 q^{41} + 16 q^{42} + 4 q^{43} + 56 q^{45} + 12 q^{46} + 28 q^{47} - 34 q^{49} - 8 q^{50} - 56 q^{51} - 4 q^{52} - 16 q^{53} + 8 q^{54} + 8 q^{56} - 28 q^{57} + 22 q^{58} - 16 q^{59} + 20 q^{62} + 24 q^{63} + 76 q^{64} + 24 q^{65} + 16 q^{67} - 12 q^{69} - 16 q^{70} + 18 q^{71} - 4 q^{73} - 8 q^{74} + 96 q^{75} - 12 q^{76} + 8 q^{77} - 80 q^{78} + 36 q^{79} + 4 q^{80} - 62 q^{81} - 32 q^{82} - 48 q^{83} + 32 q^{84} + 8 q^{85} - 20 q^{86} + 32 q^{87} - 4 q^{88} + 64 q^{89} - 40 q^{90} - 20 q^{91} - 4 q^{92} + 8 q^{93} + 72 q^{94} - 32 q^{95} - 4 q^{96} - 4 q^{97} - 40 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(946, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
946.2.e.a 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
946.2.e.b 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
946.2.e.c 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}+(-3+\cdots)q^{5}+\cdots\)
946.2.e.d 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
946.2.e.e 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
946.2.e.f 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
946.2.e.g 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
946.2.e.h 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(2\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(2-2\zeta_{6})q^{3}+q^{4}+(2-2\zeta_{6})q^{6}+\cdots\)
946.2.e.i 946.e 43.c $2$ $7.554$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(3-3\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
946.2.e.j 946.e 43.c $4$ $7.554$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(4\) \(3\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}+(2-2\beta _{1}+\cdots)q^{5}+\cdots\)
946.2.e.k 946.e 43.c $8$ $7.554$ 8.0.\(\cdots\).2 None \(8\) \(-1\) \(-4\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{2}+\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots\)
946.2.e.l 946.e 43.c $12$ $7.554$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(12\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{4}q^{6}+\cdots\)
946.2.e.m 946.e 43.c $16$ $7.554$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+\beta _{13}q^{3}+q^{4}+(\beta _{1}-\beta _{5})q^{5}+\cdots\)
946.2.e.n 946.e 43.c $18$ $7.554$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-18\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-\beta _{5}+\beta _{12})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(946, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(946, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(86, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)