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Properties

Label 1560.2.eq
Level $1560$
Weight $2$
Character orbit 1560.eq
Rep. character $\chi_{1560}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
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.eq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
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 336 1072
Cusp forms 1280 336 944
Eisenstein series 128 0 128

Trace form

\( 336 q + O(q^{10}) \) \( 336 q - 8 q^{13} - 24 q^{27} + 36 q^{33} + 72 q^{37} + 48 q^{51} + 24 q^{55} + 24 q^{63} - 72 q^{67} - 12 q^{75} + 16 q^{81} + 96 q^{85} + 64 q^{91} + 36 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)