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Properties

Label 1148.4.bi
Level $1148$
Weight $4$
Character orbit 1148.bi
Rep. character $\chi_{1148}(9,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
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.bi (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2040 336 1704
Cusp forms 1992 336 1656
Eisenstein series 48 0 48

Trace form

\( 336 q + O(q^{10}) \) \( 336 q + 28 q^{11} - 168 q^{15} + 48 q^{17} + 68 q^{19} + 4200 q^{25} + 552 q^{27} - 136 q^{29} - 176 q^{31} - 724 q^{35} + 672 q^{37} - 584 q^{41} + 1544 q^{45} + 208 q^{47} - 40 q^{51} - 824 q^{53} - 792 q^{55} - 320 q^{57} - 920 q^{59} + 5096 q^{63} + 272 q^{65} + 800 q^{67} - 696 q^{69} + 736 q^{71} - 968 q^{75} - 500 q^{79} + 12992 q^{81} + 6880 q^{83} + 4448 q^{85} + 2068 q^{89} - 1624 q^{93} - 2108 q^{95} - 3864 q^{97} - 6768 q^{99} + O(q^{100}) \)

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

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