↑

Properties

Label 3640.2.gv
Level $3640$
Weight $2$
Character orbit 3640.gv
Rep. character $\chi_{3640}(261,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $768$
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.gv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1360 768 592
Cusp forms 1328 768 560
Eisenstein series 32 0 32

Trace form

\( 768 q - 4 q^{2} + 4 q^{4} + 8 q^{8} + 384 q^{9} + O(q^{10}) \) \( 768 q - 4 q^{2} + 4 q^{4} + 8 q^{8} + 384 q^{9} + 20 q^{12} - 20 q^{14} + 20 q^{16} + 32 q^{22} + 16 q^{23} + 40 q^{24} + 384 q^{25} - 24 q^{32} + 20 q^{38} + 128 q^{42} - 44 q^{44} - 24 q^{46} + 80 q^{47} - 168 q^{48} - 8 q^{50} + 80 q^{54} - 64 q^{56} - 12 q^{58} - 28 q^{60} + 32 q^{62} + 160 q^{63} + 40 q^{64} - 100 q^{66} - 36 q^{68} - 24 q^{70} + 32 q^{71} + 64 q^{72} + 28 q^{74} + 40 q^{76} - 40 q^{78} - 80 q^{79} - 368 q^{81} + 48 q^{82} - 56 q^{84} + 84 q^{86} + 8 q^{88} - 16 q^{89} - 168 q^{92} + 120 q^{94} - 40 q^{96} + 100 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)