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Properties

Label 1520.2.t
Level $1520$
Weight $2$
Character orbit 1520.t
Rep. character $\chi_{1520}(1027,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $432$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 488 432 56
Cusp forms 472 432 40
Eisenstein series 16 0 16

Trace form

\( 432 q - 432 q^{9} + O(q^{10}) \) \( 432 q - 432 q^{9} - 16 q^{12} - 16 q^{22} + 16 q^{26} + 32 q^{28} - 24 q^{30} + 40 q^{32} + 16 q^{34} - 40 q^{40} - 80 q^{42} + 64 q^{43} - 64 q^{44} - 84 q^{48} + 60 q^{52} + 16 q^{54} - 48 q^{56} - 32 q^{58} + 32 q^{59} + 92 q^{60} - 24 q^{62} + 16 q^{66} - 96 q^{68} + 24 q^{70} - 64 q^{71} + 100 q^{72} - 16 q^{73} - 56 q^{74} - 32 q^{75} + 128 q^{78} - 16 q^{80} + 432 q^{81} - 24 q^{82} + 16 q^{86} + 108 q^{88} + 136 q^{90} - 32 q^{91} - 40 q^{92} + 16 q^{96} - 88 q^{98} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)