↑

Properties

Label 1560.2.fi
Level $1560$
Weight $2$
Character orbit 1560.fi
Rep. character $\chi_{1560}(331,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $448$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.fi (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
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 1376 448 928
Cusp forms 1312 448 864
Eisenstein series 64 0 64

Trace form

\( 448 q - 224 q^{9} + O(q^{10}) \) \( 448 q - 224 q^{9} + 32 q^{14} + 32 q^{20} + 24 q^{24} - 80 q^{26} + 56 q^{28} - 96 q^{34} + 24 q^{42} + 64 q^{44} + 8 q^{46} + 32 q^{48} - 96 q^{49} - 40 q^{52} + 64 q^{57} + 64 q^{58} - 64 q^{59} + 120 q^{62} + 48 q^{68} - 16 q^{70} + 32 q^{73} + 48 q^{74} - 144 q^{76} - 40 q^{78} + 32 q^{80} - 224 q^{81} + 120 q^{82} - 120 q^{88} + 224 q^{91} + 48 q^{92} - 8 q^{94} + 40 q^{96} + 32 q^{97} - 104 q^{98} + O(q^{100}) \)

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

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