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Properties

Label 1148.4.cc
Level $1148$
Weight $4$
Character orbit 1148.cc
Rep. character $\chi_{1148}(13,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1344$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1148.cc (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1148, [\chi])\).

Total New Old
Modular forms 8160 1344 6816
Cusp forms 7968 1344 6624
Eisenstein series 192 0 192

Trace form

\( 1344 q + 112 q^{9} + O(q^{10}) \) \( 1344 q + 112 q^{9} - 336 q^{15} - 584 q^{21} - 416 q^{29} - 200 q^{35} - 2016 q^{37} + 928 q^{43} - 1712 q^{49} + 5040 q^{51} + 256 q^{53} - 5824 q^{57} + 2440 q^{63} + 6016 q^{65} + 528 q^{67} + 3968 q^{71} + 4968 q^{77} - 3024 q^{79} + 1792 q^{85} - 3024 q^{91} - 3136 q^{93} + 4016 q^{95} + 1040 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1148, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1148, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)