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Properties

Label 1456.2.z
Level $1456$
Weight $2$
Character orbit 1456.z
Rep. character $\chi_{1456}(125,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $440$
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.z (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1456 \)
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 456 456 0
Cusp forms 440 440 0
Eisenstein series 16 16 0

Trace form

\( 440 q - 4 q^{2} - 4 q^{8} + O(q^{10}) \) \( 440 q - 4 q^{2} - 4 q^{8} + 12 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{18} - 8 q^{22} - 408 q^{25} + 12 q^{28} - 8 q^{29} + 40 q^{30} - 24 q^{32} - 4 q^{35} + 40 q^{36} + 16 q^{42} - 4 q^{44} - 32 q^{46} + 44 q^{50} - 8 q^{53} + 20 q^{56} - 24 q^{57} + 28 q^{58} + 60 q^{60} + 24 q^{63} - 48 q^{64} - 8 q^{65} + 20 q^{70} + 68 q^{72} + 48 q^{74} + 28 q^{77} + 100 q^{78} - 16 q^{79} - 392 q^{81} + 88 q^{84} - 100 q^{86} + 64 q^{88} + 52 q^{91} - 40 q^{92} + 76 q^{98} + 88 q^{99} + O(q^{100}) \)

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.