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Properties

Label 1560.2.cb
Level $1560$
Weight $2$
Character orbit 1560.cb
Rep. character $\chi_{1560}(811,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $224$
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.cb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 688 224 464
Cusp forms 656 224 432
Eisenstein series 32 0 32

Trace form

\( 224 q + 224 q^{9} + O(q^{10}) \) \( 224 q + 224 q^{9} - 32 q^{14} + 16 q^{20} - 24 q^{24} - 40 q^{26} + 64 q^{28} + 48 q^{34} + 48 q^{42} + 56 q^{44} - 8 q^{46} + 64 q^{48} + 40 q^{52} + 32 q^{57} + 32 q^{58} + 64 q^{59} - 48 q^{68} + 16 q^{70} - 32 q^{73} - 48 q^{74} + 24 q^{76} + 40 q^{78} - 32 q^{80} + 224 q^{81} - 48 q^{86} - 32 q^{91} - 192 q^{92} - 16 q^{94} - 40 q^{96} - 32 q^{97} - 112 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)