↑

Properties

Label 3640.2.oh
Level $3640$
Weight $2$
Character orbit 3640.oh
Rep. character $\chi_{3640}(509,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2656$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.oh (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

\( 2656 q - 24 q^{6} + 1304 q^{9} + O(q^{10}) \) \( 2656 q - 24 q^{6} + 1304 q^{9} - 6 q^{10} - 4 q^{15} - 8 q^{16} - 24 q^{20} - 12 q^{24} - 12 q^{26} - 6 q^{30} - 24 q^{31} + 24 q^{34} + 12 q^{36} - 56 q^{39} + 48 q^{40} - 52 q^{44} + 4 q^{46} - 24 q^{49} - 36 q^{50} + 12 q^{54} - 12 q^{56} + 42 q^{60} - 4 q^{65} + 12 q^{66} - 64 q^{71} - 8 q^{74} - 48 q^{76} - 16 q^{79} + 162 q^{80} - 1216 q^{81} + 108 q^{84} - 48 q^{86} - 24 q^{89} + 72 q^{90} - 12 q^{94} - 12 q^{96} + O(q^{100}) \)

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.