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Properties

Label 1520.2.dy
Level $1520$
Weight $2$
Character orbit 1520.dy
Rep. character $\chi_{1520}(33,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $696$
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.dy (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 3024 744 2280
Cusp forms 2736 696 2040
Eisenstein series 288 48 240

Trace form

\( 696 q + 12 q^{3} - 12 q^{5} + 6 q^{7} + O(q^{10}) \) \( 696 q + 12 q^{3} - 12 q^{5} + 6 q^{7} + 12 q^{11} - 12 q^{13} + 12 q^{15} - 12 q^{17} - 24 q^{21} + 12 q^{23} - 12 q^{25} + 18 q^{27} + 36 q^{31} + 6 q^{33} + 12 q^{35} - 48 q^{41} + 12 q^{43} - 6 q^{45} + 48 q^{47} + 48 q^{51} - 12 q^{53} - 90 q^{55} - 12 q^{57} - 24 q^{61} - 54 q^{63} - 18 q^{65} + 156 q^{67} + 24 q^{71} - 12 q^{73} + 60 q^{77} - 24 q^{81} + 42 q^{83} - 12 q^{85} + 78 q^{87} + 24 q^{91} - 30 q^{93} + 12 q^{95} - 12 q^{97} + O(q^{100}) \)

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

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