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Properties

Label 946.2.f
Level $946$
Weight $2$
Character orbit 946.f
Rep. character $\chi_{946}(345,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $168$
Newform subspaces $8$
Sturm bound $264$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 946 = 2 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 946.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 8 \)
Sturm bound: \(264\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 544 168 376
Cusp forms 512 168 344
Eisenstein series 32 0 32

Trace form

\( 168 q + 4 q^{3} - 42 q^{4} + 4 q^{5} + 4 q^{6} + 8 q^{7} - 62 q^{9} + O(q^{10}) \) \( 168 q + 4 q^{3} - 42 q^{4} + 4 q^{5} + 4 q^{6} + 8 q^{7} - 62 q^{9} - 8 q^{10} + 4 q^{11} - 16 q^{12} - 2 q^{13} - 4 q^{14} - 28 q^{15} - 42 q^{16} + 16 q^{18} + 8 q^{19} + 4 q^{20} + 24 q^{21} + 16 q^{22} + 12 q^{23} + 4 q^{24} - 46 q^{25} - 16 q^{26} + 4 q^{27} - 12 q^{28} - 32 q^{29} + 16 q^{30} + 4 q^{31} + 36 q^{33} + 40 q^{35} - 22 q^{36} + 52 q^{37} + 8 q^{38} - 44 q^{39} - 8 q^{40} - 4 q^{41} - 4 q^{42} - 8 q^{43} + 14 q^{44} - 48 q^{45} + 24 q^{46} - 6 q^{47} + 4 q^{48} + 2 q^{49} + 32 q^{50} - 32 q^{51} + 8 q^{52} - 64 q^{54} - 16 q^{55} + 16 q^{56} - 48 q^{57} - 32 q^{58} + 24 q^{59} + 32 q^{60} - 32 q^{61} - 12 q^{62} - 4 q^{63} - 42 q^{64} - 40 q^{65} - 48 q^{66} - 76 q^{67} + 96 q^{69} + 52 q^{70} + 12 q^{71} - 24 q^{72} - 72 q^{73} + 28 q^{74} + 20 q^{75} + 8 q^{76} - 32 q^{77} + 40 q^{78} + 80 q^{79} + 4 q^{80} - 106 q^{81} + 32 q^{82} + 8 q^{83} - 16 q^{84} + 24 q^{85} + 96 q^{87} - 4 q^{88} - 80 q^{89} - 56 q^{90} - 8 q^{91} - 28 q^{92} - 20 q^{93} - 72 q^{94} + 96 q^{95} + 4 q^{96} + 46 q^{97} + 16 q^{98} + 14 q^{99} + O(q^{100}) \)

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.f.a 946.f 11.c $4$ $7.554$ \(\Q(\zeta_{10})\) None \(-1\) \(-6\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
946.2.f.b 946.f 11.c $4$ $7.554$ \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(3\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots\)
946.2.f.c 946.f 11.c $8$ $7.554$ 8.0.13140625.1 None \(-2\) \(7\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{3}-\beta _{4}-\beta _{7})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
946.2.f.d 946.f 11.c $16$ $7.554$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(4\) \(9\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{5}q^{2}-\beta _{9}q^{3}+\beta _{10}q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
946.2.f.e 946.f 11.c $24$ $7.554$ None \(6\) \(-1\) \(-11\) \(3\) $\mathrm{SU}(2)[C_{5}]$
946.2.f.f 946.f 11.c $32$ $7.554$ None \(-8\) \(-2\) \(2\) \(10\) $\mathrm{SU}(2)[C_{5}]$
946.2.f.g 946.f 11.c $40$ $7.554$ None \(-10\) \(5\) \(8\) \(5\) $\mathrm{SU}(2)[C_{5}]$
946.2.f.h 946.f 11.c $40$ $7.554$ None \(10\) \(-1\) \(-5\) \(1\) $\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(946, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)