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Properties

Label 1248.2.dz
Level $1248$
Weight $2$
Character orbit 1248.dz
Rep. character $\chi_{1248}(179,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1760$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1248.dz (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1248 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

Total New Old
Modular forms 1824 1824 0
Cusp forms 1760 1760 0
Eisenstein series 64 64 0

Trace form

\( 1760 q - 4 q^{3} - 8 q^{4} - 12 q^{6} - 24 q^{7} - 4 q^{9} + O(q^{10}) \) \( 1760 q - 4 q^{3} - 8 q^{4} - 12 q^{6} - 24 q^{7} - 4 q^{9} - 8 q^{10} - 16 q^{12} - 16 q^{13} - 24 q^{15} - 8 q^{16} - 24 q^{19} + 8 q^{22} - 12 q^{24} - 32 q^{25} - 64 q^{27} - 24 q^{28} + 12 q^{30} - 24 q^{33} + 8 q^{36} - 24 q^{37} + 40 q^{39} - 32 q^{40} - 44 q^{42} - 8 q^{43} - 12 q^{45} - 24 q^{46} - 56 q^{48} + 8 q^{51} - 56 q^{52} - 12 q^{54} - 40 q^{55} - 24 q^{58} - 8 q^{61} - 32 q^{64} + 128 q^{66} - 24 q^{67} - 4 q^{69} - 12 q^{72} - 24 q^{75} - 24 q^{76} - 148 q^{78} - 64 q^{79} + 72 q^{82} - 12 q^{84} + 96 q^{85} - 4 q^{87} + 32 q^{88} - 160 q^{90} - 64 q^{91} - 48 q^{93} - 48 q^{94} - 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces

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