Properties

Label 2520.2.j
Level $2520$
Weight $2$
Character orbit 2520.j
Rep. character $\chi_{2520}(2269,\cdot)$
Character field $\Q$
Dimension $180$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.j (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 \(M_{2}(2520, [\chi])\).

Total New Old
Modular forms 592 180 412
Cusp forms 560 180 380
Eisenstein series 32 0 32

Trace form

\( 180 q - 4 q^{4} + O(q^{10}) \) \( 180 q - 4 q^{4} + 8 q^{10} - 20 q^{16} + 4 q^{20} + 4 q^{25} - 36 q^{26} + 16 q^{31} + 12 q^{34} + 32 q^{40} - 8 q^{41} + 24 q^{44} - 180 q^{49} + 60 q^{50} + 32 q^{55} + 12 q^{56} + 20 q^{64} - 24 q^{65} + 12 q^{70} - 56 q^{71} + 32 q^{74} + 48 q^{76} + 56 q^{79} + 4 q^{80} + 64 q^{86} - 40 q^{89} + 20 q^{94} + 40 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2520, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)