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Properties

Label 3136.2.cg
Level $3136$
Weight $2$
Character orbit 3136.cg
Rep. character $\chi_{3136}(19,\cdot)$
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.cg (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

\( 5056 q + 8 q^{2} + 24 q^{3} + 8 q^{4} + 24 q^{5} - 64 q^{8} + 8 q^{9} + O(q^{10}) \) \( 5056 q + 8 q^{2} + 24 q^{3} + 8 q^{4} + 24 q^{5} - 64 q^{8} + 8 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{12} - 64 q^{15} + 8 q^{16} + 24 q^{17} + 8 q^{18} + 24 q^{19} - 32 q^{22} + 8 q^{23} + 24 q^{24} + 8 q^{25} + 24 q^{26} - 64 q^{29} - 152 q^{30} + 48 q^{31} + 8 q^{32} + 256 q^{36} + 8 q^{37} + 24 q^{38} + 8 q^{39} + 24 q^{40} - 64 q^{43} - 8 q^{44} + 24 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{50} + 8 q^{51} - 120 q^{52} + 8 q^{53} + 24 q^{54} - 64 q^{57} + 8 q^{58} + 216 q^{59} - 184 q^{60} + 24 q^{61} + 128 q^{64} + 16 q^{65} - 264 q^{66} + 168 q^{67} + 24 q^{68} - 192 q^{71} + 8 q^{72} + 24 q^{73} - 104 q^{74} + 24 q^{75} + 32 q^{78} + 8 q^{79} - 48 q^{80} + 8 q^{81} + 264 q^{82} - 64 q^{85} + 8 q^{86} + 24 q^{87} + 8 q^{88} + 24 q^{89} - 64 q^{92} - 88 q^{93} + 24 q^{94} + 16 q^{95} + 432 q^{96} - 112 q^{99} + O(q^{100}) \)

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

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