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Properties

Label 1248.2.ck
Level $1248$
Weight $2$
Character orbit 1248.ck
Rep. character $\chi_{1248}(157,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $384$
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.ck (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 912 384 528
Cusp forms 880 384 496
Eisenstein series 32 0 32

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 16 q^{10} + 16 q^{12} + 16 q^{16} + 16 q^{18} + 32 q^{23} + 16 q^{24} + 96 q^{31} + 96 q^{35} + 64 q^{40} + 32 q^{43} - 16 q^{44} - 48 q^{50} - 32 q^{51} + 64 q^{53} - 16 q^{54} - 32 q^{55} - 112 q^{56} + 64 q^{58} + 64 q^{61} - 48 q^{62} - 32 q^{63} - 48 q^{64} - 96 q^{66} - 32 q^{67} + 64 q^{68} + 64 q^{69} + 64 q^{74} - 32 q^{75} - 16 q^{76} + 64 q^{77} + 112 q^{80} + 160 q^{82} + 176 q^{88} + 16 q^{92} + 16 q^{94} + 160 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)