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Properties

Label 3136.2.ch
Level $3136$
Weight $2$
Character orbit 3136.ch
Rep. character $\chi_{3136}(165,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $5056$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.ch (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3136, [\chi])\).

Total New Old
Modular forms 7296 5184 2112
Cusp forms 7040 5056 1984
Eisenstein series 256 128 128

Trace form

\( 5056 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{5} + 32 q^{6} - 64 q^{8} + 8 q^{9} + O(q^{10}) \) \( 5056 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{5} + 32 q^{6} - 64 q^{8} + 8 q^{9} + 8 q^{10} + 8 q^{11} + 8 q^{12} + 32 q^{13} - 64 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 8 q^{19} + 32 q^{20} - 96 q^{22} + 8 q^{23} + 88 q^{24} + 8 q^{25} + 8 q^{26} + 32 q^{27} - 64 q^{29} + 168 q^{30} + 8 q^{32} + 32 q^{34} - 384 q^{36} + 8 q^{37} + 88 q^{38} + 8 q^{39} + 8 q^{40} + 32 q^{41} - 64 q^{43} + 24 q^{44} + 8 q^{45} + 8 q^{46} + 8 q^{47} + 32 q^{48} - 112 q^{50} + 8 q^{51} + 56 q^{52} + 8 q^{53} + 8 q^{54} + 32 q^{55} - 64 q^{57} + 8 q^{58} - 56 q^{59} - 184 q^{60} + 8 q^{61} + 64 q^{62} - 256 q^{64} + 16 q^{65} + 136 q^{66} + 168 q^{67} + 8 q^{68} + 32 q^{69} + 64 q^{71} + 8 q^{72} + 8 q^{73} - 104 q^{74} + 8 q^{75} + 32 q^{76} - 160 q^{78} + 8 q^{79} + 32 q^{80} + 8 q^{81} - 72 q^{82} + 32 q^{83} - 64 q^{85} + 8 q^{86} + 8 q^{87} + 8 q^{88} + 8 q^{89} + 320 q^{90} - 64 q^{92} - 88 q^{93} + 8 q^{94} - 128 q^{96} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)