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Properties

Label 1520.2.bk
Level $1520$
Weight $2$
Character orbit 1520.bk
Rep. character $\chi_{1520}(531,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $320$
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.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 488 320 168
Cusp forms 472 320 152
Eisenstein series 16 0 16

Trace form

\( 320 q + O(q^{10}) \) \( 320 q - 8 q^{16} - 8 q^{19} + 8 q^{24} - 16 q^{26} - 40 q^{28} - 32 q^{36} + 20 q^{38} - 80 q^{42} + 88 q^{44} + 320 q^{49} - 120 q^{54} - 56 q^{58} - 32 q^{61} - 64 q^{62} + 48 q^{64} - 48 q^{66} + 16 q^{68} + 152 q^{74} + 32 q^{76} - 16 q^{80} - 320 q^{81} - 80 q^{82} + 32 q^{85} - 24 q^{92} - 160 q^{96} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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