↑

Properties

Label 1456.2.fh
Level $1456$
Weight $2$
Character orbit 1456.fh
Rep. character $\chi_{1456}(373,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $880$
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.fh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1456 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 912 912 0
Cusp forms 880 880 0
Eisenstein series 32 32 0

Trace form

\( 880 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 4 q^{5} - 4 q^{6} - 16 q^{8} + O(q^{10}) \) \( 880 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 4 q^{5} - 4 q^{6} - 16 q^{8} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 8 q^{15} + 2 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} + 4 q^{20} - 2 q^{21} - 16 q^{22} - 4 q^{24} - 2 q^{26} - 4 q^{27} - 52 q^{28} - 4 q^{29} + 12 q^{30} - 8 q^{31} + 2 q^{32} - 8 q^{33} - 24 q^{34} + 8 q^{35} + 12 q^{36} + 2 q^{37} - 24 q^{38} - 24 q^{40} - 46 q^{42} - 4 q^{43} - 12 q^{44} + 10 q^{45} - 24 q^{46} - 8 q^{47} - 44 q^{48} - 4 q^{49} - 8 q^{50} - 16 q^{51} + 4 q^{52} - 4 q^{53} + 26 q^{54} + 32 q^{56} - 4 q^{58} + 18 q^{59} - 20 q^{60} - 4 q^{61} + 36 q^{62} + 108 q^{63} - 16 q^{64} - 4 q^{65} + 8 q^{66} - 4 q^{67} + 54 q^{68} + 8 q^{69} - 28 q^{70} + 140 q^{72} + 30 q^{74} + 24 q^{75} - 4 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} - 4 q^{80} - 760 q^{81} + 60 q^{82} - 16 q^{83} + 88 q^{84} + 6 q^{85} + 12 q^{86} - 4 q^{88} - 4 q^{90} - 10 q^{91} + 72 q^{92} - 10 q^{93} - 12 q^{94} + 4 q^{95} - 128 q^{96} - 8 q^{97} + 24 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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