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Properties

Label 3696.2.gz
Level $3696$
Weight $2$
Character orbit 3696.gz
Rep. character $\chi_{3696}(179,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $12160$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3696.gz (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3696 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3696, [\chi])\).

Total New Old
Modular forms 12416 12416 0
Cusp forms 12160 12160 0
Eisenstein series 256 256 0

Trace form

\( 12160 q - 6 q^{3} - 12 q^{4} - 24 q^{6} - 48 q^{7} + O(q^{10}) \) \( 12160 q - 6 q^{3} - 12 q^{4} - 24 q^{6} - 48 q^{7} - 32 q^{10} - 16 q^{12} - 48 q^{13} + 20 q^{16} - 22 q^{18} - 12 q^{19} - 44 q^{21} - 160 q^{22} - 6 q^{24} - 24 q^{27} - 32 q^{28} + 2 q^{30} - 16 q^{33} - 96 q^{34} + 8 q^{36} - 12 q^{37} - 12 q^{39} - 12 q^{40} + 16 q^{42} - 128 q^{43} - 56 q^{45} - 60 q^{46} + 56 q^{48} - 48 q^{49} + 18 q^{51} - 36 q^{52} - 48 q^{54} - 128 q^{55} + 20 q^{58} - 106 q^{60} - 12 q^{61} - 192 q^{64} + 32 q^{67} - 60 q^{69} + 60 q^{70} + 26 q^{72} + 38 q^{75} - 128 q^{76} - 48 q^{78} - 12 q^{81} + 4 q^{82} - 114 q^{84} + 32 q^{85} - 32 q^{87} - 132 q^{90} + 160 q^{91} + 18 q^{93} + 76 q^{94} - 6 q^{96} - 96 q^{97} - 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3696, [\chi])\) into newform subspaces

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