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Properties

Label 1456.2.fw
Level $1456$
Weight $2$
Character orbit 1456.fw
Rep. character $\chi_{1456}(251,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $880$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.fw (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

\( 880 q - 12 q^{2} - 4 q^{4} - 12 q^{7} + O(q^{10}) \) \( 880 q - 12 q^{2} - 4 q^{4} - 12 q^{7} - 12 q^{11} - 32 q^{14} - 4 q^{16} - 28 q^{22} - 8 q^{23} - 4 q^{29} + 12 q^{30} - 12 q^{32} - 12 q^{35} - 36 q^{36} - 12 q^{37} - 16 q^{39} + 62 q^{42} - 4 q^{43} - 72 q^{46} - 4 q^{49} + 12 q^{50} - 40 q^{51} - 16 q^{53} - 8 q^{56} - 12 q^{58} - 16 q^{64} - 16 q^{65} - 12 q^{67} - 24 q^{71} - 108 q^{72} - 32 q^{74} - 36 q^{77} - 120 q^{78} + 368 q^{81} + 36 q^{84} - 72 q^{85} - 4 q^{88} - 46 q^{91} + 160 q^{92} + 24 q^{93} + 48 q^{98} + O(q^{100}) \)

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.