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Properties

Label 1520.2.bz
Level $1520$
Weight $2$
Character orbit 1520.bz
Rep. character $\chi_{1520}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
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.bz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 504 124 380
Cusp forms 456 116 340
Eisenstein series 48 8 40

Trace form

\( 116 q - q^{5} + 52 q^{9} + O(q^{10}) \) \( 116 q - q^{5} + 52 q^{9} + 8 q^{11} + 7 q^{15} + 8 q^{19} + 4 q^{21} - q^{25} - 2 q^{29} - 24 q^{31} - 22 q^{35} + 20 q^{39} + 2 q^{41} - 92 q^{49} - 6 q^{51} - 12 q^{55} + 38 q^{59} + 14 q^{61} - 30 q^{65} + 12 q^{69} + 30 q^{71} + 30 q^{75} + 14 q^{79} - 6 q^{81} - 19 q^{85} - 6 q^{89} + 12 q^{91} + 19 q^{95} + 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)