Properties

Label 1456.2.y
Level $1456$
Weight $2$
Character orbit 1456.y
Rep. character $\chi_{1456}(827,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $336$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

Total New Old
Modular forms 456 336 120
Cusp forms 440 336 104
Eisenstein series 16 0 16

Trace form

\( 336 q + 12 q^{6} + 12 q^{8} + O(q^{10}) \) \( 336 q + 12 q^{6} + 12 q^{8} + 16 q^{10} - 12 q^{18} - 20 q^{20} - 16 q^{22} + 32 q^{24} - 336 q^{25} - 32 q^{26} + 40 q^{32} - 20 q^{34} + 64 q^{36} + 40 q^{38} + 32 q^{43} + 52 q^{44} - 32 q^{46} + 32 q^{50} - 16 q^{54} + 64 q^{55} - 92 q^{58} + 76 q^{60} + 72 q^{64} + 24 q^{68} - 24 q^{70} - 12 q^{72} + 16 q^{73} + 56 q^{74} + 32 q^{75} - 20 q^{76} + 116 q^{78} - 336 q^{81} + 40 q^{82} + 28 q^{84} - 20 q^{86} + 16 q^{89} - 24 q^{92} + 96 q^{93} - 64 q^{94} - 32 q^{96} - 128 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)