Properties

Label 2520.2.fn
Level $2520$
Weight $2$
Character orbit 2520.fn
Rep. character $\chi_{2520}(781,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $768$
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.fn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2520, [\chi])\).

Total New Old
Modular forms 1168 768 400
Cusp forms 1136 768 368
Eisenstein series 32 0 32

Trace form

\( 768 q + O(q^{10}) \) \( 768 q - 10 q^{12} - 10 q^{14} + 10 q^{18} - 20 q^{24} + 384 q^{25} - 40 q^{32} + 40 q^{36} + 20 q^{38} + 52 q^{42} - 22 q^{44} + 160 q^{47} + 4 q^{48} - 10 q^{54} - 12 q^{56} - 28 q^{60} - 88 q^{62} - 80 q^{63} + 48 q^{66} + 10 q^{68} - 50 q^{72} + 8 q^{78} + 16 q^{81} + 100 q^{84} + 18 q^{86} - 8 q^{89} + 18 q^{90} + 76 q^{92} - 118 q^{96} + 78 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)