↑

Properties

Label 2760.2.f
Level $2760$
Weight $2$
Character orbit 2760.f
Rep. character $\chi_{2760}(829,\cdot)$
Character field $\Q$
Dimension $264$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2760.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2760, [\chi])\).

Total New Old
Modular forms 584 264 320
Cusp forms 568 264 304
Eisenstein series 16 0 16

Trace form

\( 264 q + 264 q^{9} + O(q^{10}) \) \( 264 q + 264 q^{9} + 20 q^{10} + 40 q^{14} - 12 q^{20} - 8 q^{25} + 16 q^{26} - 8 q^{30} + 48 q^{31} - 16 q^{34} + 32 q^{39} - 20 q^{40} + 16 q^{41} - 40 q^{44} - 264 q^{49} - 16 q^{50} + 32 q^{55} + 16 q^{56} + 24 q^{60} + 48 q^{64} + 48 q^{65} - 40 q^{66} - 32 q^{70} - 64 q^{71} - 88 q^{74} + 48 q^{76} + 28 q^{80} + 264 q^{81} - 24 q^{84} - 16 q^{86} + 80 q^{89} + 20 q^{90} - 64 q^{94} - 48 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2760, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)