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Properties

Label 1148.4.ca
Level $1148$
Weight $4$
Character orbit 1148.ca
Rep. character $\chi_{1148}(15,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $6048$
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.ca (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
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 8128 6048 2080
Cusp forms 8000 6048 1952
Eisenstein series 128 0 128

Trace form

\( 6048 q - 120 q^{6} - 80 q^{9} + O(q^{10}) \) \( 6048 q - 120 q^{6} - 80 q^{9} - 408 q^{12} + 216 q^{17} - 568 q^{29} + 1632 q^{30} + 920 q^{32} - 2320 q^{33} - 1000 q^{34} - 2040 q^{36} - 2360 q^{41} + 560 q^{42} - 1160 q^{52} + 1144 q^{53} + 3240 q^{54} - 2440 q^{60} + 1560 q^{61} + 984 q^{62} - 25440 q^{66} - 3240 q^{72} + 3928 q^{74} + 19528 q^{78} + 25280 q^{80} + 2592 q^{85} + 24400 q^{86} + 29096 q^{88} + 3760 q^{89} - 4792 q^{92} - 30432 q^{94} - 17152 q^{96} + 9080 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1148, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)