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Properties

Label 2520.2.dp
Level $2520$
Weight $2$
Character orbit 2520.dp
Rep. character $\chi_{2520}(169,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
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.dp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 1184 216 968
Cusp forms 1120 216 904
Eisenstein series 64 0 64

Trace form

\( 216 q + O(q^{10}) \) \( 216 q - 24 q^{11} + 4 q^{15} - 24 q^{29} + 16 q^{39} - 36 q^{45} + 108 q^{49} + 60 q^{51} - 24 q^{59} - 24 q^{65} + 40 q^{69} + 24 q^{71} + 32 q^{75} + 80 q^{81} - 24 q^{85} + 28 q^{95} + 92 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)