Properties

Label 1520.2.em
Level $1520$
Weight $2$
Character orbit 1520.em
Rep. character $\chi_{1520}(61,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1920$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.em (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1520, [\chi])\).

Total New Old
Modular forms 2928 1920 1008
Cusp forms 2832 1920 912
Eisenstein series 96 0 96

Trace form

\( 1920q + O(q^{10}) \) \( 1920q - 12q^{10} + 12q^{16} + 48q^{26} + 120q^{34} + 48q^{36} - 60q^{38} + 240q^{42} - 132q^{44} - 60q^{46} + 960q^{49} - 24q^{51} - 96q^{52} - 180q^{54} + 120q^{66} - 72q^{68} + 48q^{69} + 168q^{72} + 168q^{74} + 96q^{76} - 96q^{85} - 108q^{90} - 312q^{96} - 84q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1520, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)