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Properties

Label 946.2.bc
Level $946$
Weight $2$
Character orbit 946.bc
Rep. character $\chi_{946}(9,\cdot)$
Character field $\Q(\zeta_{105})$
Dimension $2112$
Newform subspaces $2$
Sturm bound $264$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 946 = 2 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 946.bc (of order \(105\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{105})\)
Newform subspaces: \( 2 \)
Sturm bound: \(264\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 6528 2112 4416
Cusp forms 6144 2112 4032
Eisenstein series 384 0 384

Trace form

\( 2112 q + 4 q^{2} - 4 q^{3} + 88 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{7} + 4 q^{8} - 48 q^{9} + O(q^{10}) \) \( 2112 q + 4 q^{2} - 4 q^{3} + 88 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{7} + 4 q^{8} - 48 q^{9} - 22 q^{11} - 4 q^{12} + 46 q^{13} + 64 q^{15} + 88 q^{16} - 8 q^{17} - 68 q^{19} - 8 q^{20} + 15 q^{22} - 40 q^{23} - 15 q^{24} - 64 q^{25} + 10 q^{26} - 28 q^{27} + 4 q^{28} - 12 q^{29} - 26 q^{30} - 6 q^{31} - 16 q^{32} + 7 q^{33} - 86 q^{34} + 64 q^{35} + 270 q^{36} + 64 q^{37} - 86 q^{38} + 64 q^{39} + 4 q^{41} - 8 q^{42} - 262 q^{43} - 180 q^{45} - 20 q^{46} - 16 q^{47} - 4 q^{48} + 238 q^{49} + 72 q^{50} + 12 q^{51} + 20 q^{52} - 62 q^{53} - 28 q^{54} - 16 q^{55} + 19 q^{57} - 6 q^{58} + 186 q^{59} - 12 q^{60} - 52 q^{61} + 104 q^{62} + 198 q^{63} + 88 q^{64} - 44 q^{65} + 88 q^{66} + 42 q^{67} - 50 q^{68} - 68 q^{69} - 72 q^{70} - 42 q^{71} - 10 q^{72} + 94 q^{73} + 4 q^{74} + 310 q^{75} + 86 q^{76} - 52 q^{77} - 184 q^{78} + 12 q^{79} + 12 q^{80} - 181 q^{81} + 98 q^{82} - 11 q^{83} - 480 q^{85} + 107 q^{86} + 384 q^{87} + 15 q^{88} + 102 q^{89} - 32 q^{90} - 32 q^{91} + 24 q^{92} - 144 q^{93} + 48 q^{94} - 116 q^{95} - 4 q^{96} + 122 q^{97} + 40 q^{98} - 323 q^{99} + O(q^{100}) \)

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.bc.a 946.bc 473.ac $1008$ $7.554$ None \(-42\) \(0\) \(-4\) \(-3\) $\mathrm{SU}(2)[C_{105}]$
946.2.bc.b 946.bc 473.ac $1104$ $7.554$ None \(46\) \(-4\) \(-4\) \(-3\) $\mathrm{SU}(2)[C_{105}]$

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

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