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Properties

Label 1148.4.k
Level $1148$
Weight $4$
Character orbit 1148.k
Rep. character $\chi_{1148}(337,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $124$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1020 124 896
Cusp forms 996 124 872
Eisenstein series 24 0 24

Trace form

\( 124 q - 4 q^{3} + O(q^{10}) \) \( 124 q - 4 q^{3} + 140 q^{11} - 96 q^{13} + 48 q^{15} + 12 q^{17} - 228 q^{19} - 208 q^{23} - 3636 q^{25} - 496 q^{27} - 48 q^{29} + 640 q^{31} + 56 q^{35} - 392 q^{37} + 152 q^{41} + 1520 q^{45} - 440 q^{47} - 872 q^{51} - 448 q^{53} + 1232 q^{55} + 824 q^{57} + 112 q^{63} - 656 q^{65} - 1868 q^{67} + 3760 q^{69} - 584 q^{71} - 3196 q^{75} + 1760 q^{79} - 11188 q^{81} + 8056 q^{83} + 2040 q^{85} - 2588 q^{89} - 1768 q^{93} - 8704 q^{95} - 3108 q^{97} + 2100 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1148, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)