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Properties

Label 1148.4.bk
Level $1148$
Weight $4$
Character orbit 1148.bk
Rep. character $\chi_{1148}(37,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $672$
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.bk (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 4080 672 3408
Cusp forms 3984 672 3312
Eisenstein series 96 0 96

Trace form

\( 672 q - 20 q^{5} - 3052 q^{9} + O(q^{10}) \) \( 672 q - 20 q^{5} - 3052 q^{9} + 28 q^{11} + 168 q^{15} - 48 q^{17} - 68 q^{19} - 616 q^{21} - 6 q^{23} + 2092 q^{25} + 552 q^{27} - 452 q^{29} - 88 q^{31} + 504 q^{33} + 796 q^{35} + 216 q^{37} - 140 q^{39} + 1384 q^{41} + 168 q^{43} - 152 q^{45} - 148 q^{47} - 748 q^{49} - 846 q^{51} - 1044 q^{53} + 168 q^{55} + 344 q^{57} - 2644 q^{59} - 966 q^{61} - 192 q^{63} - 2742 q^{65} - 1852 q^{67} - 5036 q^{69} + 3828 q^{71} + 1952 q^{73} - 3306 q^{75} - 1236 q^{77} - 668 q^{79} - 27424 q^{81} - 5504 q^{83} - 4448 q^{85} + 1856 q^{87} + 1598 q^{89} - 228 q^{91} + 3812 q^{93} + 850 q^{95} - 2496 q^{97} + 6272 q^{99} + O(q^{100}) \)

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

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