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Properties

Label 1560.2.gc
Level $1560$
Weight $2$
Character orbit 1560.gc
Rep. character $\chi_{1560}(97,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $168$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.gc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 1408 168 1240
Cusp forms 1280 168 1112
Eisenstein series 128 0 128

Trace form

\( 168 q - 8 q^{5} + O(q^{10}) \) \( 168 q - 8 q^{5} + 8 q^{11} + 8 q^{13} - 12 q^{17} - 8 q^{19} + 4 q^{25} + 8 q^{31} + 12 q^{37} + 8 q^{39} + 44 q^{41} + 8 q^{45} + 60 q^{49} - 12 q^{53} + 24 q^{55} + 8 q^{59} + 28 q^{65} + 8 q^{67} - 56 q^{73} - 48 q^{77} + 84 q^{81} - 44 q^{85} + 72 q^{87} + 4 q^{89} - 32 q^{95} + 40 q^{97} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)