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Properties

Label 1148.4.y
Level $1148$
Weight $4$
Character orbit 1148.y
Rep. character $\chi_{1148}(407,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1512$
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.y (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2032 1512 520
Cusp forms 2000 1512 488
Eisenstein series 32 0 32

Trace form

\( 1512 q + 120 q^{6} + 80 q^{9} + O(q^{10}) \) \( 1512 q + 120 q^{6} + 80 q^{9} + 408 q^{12} - 216 q^{17} + 568 q^{29} - 1632 q^{30} - 920 q^{32} + 2320 q^{33} + 1000 q^{34} + 2040 q^{36} + 2360 q^{41} - 560 q^{42} + 1160 q^{52} - 1144 q^{53} - 3240 q^{54} + 2440 q^{60} - 1560 q^{61} - 984 q^{62} + 2072 q^{74} + 8072 q^{78} + 6320 q^{80} - 2592 q^{85} - 13496 q^{88} - 3760 q^{89} - 2168 q^{92} + 3432 q^{94} + 17152 q^{96} - 9080 q^{97} + O(q^{100}) \)

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

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