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Properties

Label 3640.2.na
Level $3640$
Weight $2$
Character orbit 3640.na
Rep. character $\chi_{3640}(1123,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2656$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.na (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3640 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

Total New Old
Modular forms 2720 2720 0
Cusp forms 2656 2656 0
Eisenstein series 64 64 0

Trace form

\( 2656 q - 24 q^{3} + O(q^{10}) \) \( 2656 q - 24 q^{3} - 8 q^{11} - 8 q^{16} - 8 q^{18} - 16 q^{22} + 36 q^{24} - 12 q^{26} - 24 q^{28} - 8 q^{30} - 16 q^{35} - 132 q^{40} + 4 q^{42} - 8 q^{44} - 4 q^{46} + 20 q^{50} - 84 q^{52} - 24 q^{54} - 60 q^{58} + 96 q^{59} + 24 q^{60} - 24 q^{65} - 24 q^{66} - 12 q^{68} - 6 q^{70} + 52 q^{72} - 88 q^{78} + 162 q^{80} + 1184 q^{81} - 24 q^{82} + 88 q^{84} + 24 q^{86} + 32 q^{88} + 16 q^{91} - 48 q^{92} - 12 q^{96} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

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