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Properties

Label 3696.2.hj
Level $3696$
Weight $2$
Character orbit 3696.hj
Rep. character $\chi_{3696}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $6144$
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.hj (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
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 6144 6272
Cusp forms 12160 6144 6016
Eisenstein series 256 0 256

Trace form

\( 6144 q - 8 q^{4} + O(q^{10}) \) \( 6144 q - 8 q^{4} - 8 q^{11} - 32 q^{14} + 8 q^{16} - 12 q^{18} + 32 q^{20} + 88 q^{22} - 24 q^{28} + 64 q^{29} + 48 q^{37} - 32 q^{43} + 4 q^{44} + 112 q^{50} - 24 q^{52} - 48 q^{53} - 8 q^{58} - 32 q^{59} + 24 q^{60} - 32 q^{64} - 24 q^{66} + 16 q^{67} + 32 q^{70} + 12 q^{72} - 32 q^{74} - 144 q^{78} + 264 q^{80} - 768 q^{81} + 72 q^{84} + 196 q^{86} - 48 q^{88} - 104 q^{91} - 376 q^{92} + 120 q^{94} + 352 q^{98} - 64 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3696, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)