Properties

Label 1122.2.bi
Level $1122$
Weight $2$
Character orbit 1122.bi
Rep. character $\chi_{1122}(25,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $576$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1122.bi (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1122, [\chi])\).

Total New Old
Modular forms 3584 576 3008
Cusp forms 3328 576 2752
Eisenstein series 256 0 256

Trace form

\( 576 q - 32 q^{5} + O(q^{10}) \) \( 576 q - 32 q^{5} + 16 q^{11} + 32 q^{14} + 144 q^{16} + 48 q^{17} + 16 q^{22} + 32 q^{23} + 32 q^{25} - 32 q^{28} + 80 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{37} + 32 q^{39} - 16 q^{42} + 32 q^{43} - 16 q^{44} - 32 q^{46} + 80 q^{49} - 80 q^{52} - 32 q^{53} + 96 q^{57} - 16 q^{58} + 32 q^{59} + 112 q^{61} - 128 q^{65} + 64 q^{66} + 96 q^{67} - 48 q^{69} + 32 q^{73} + 64 q^{75} - 16 q^{77} - 32 q^{79} - 48 q^{80} - 64 q^{83} + 32 q^{84} + 80 q^{85} + 64 q^{86} + 16 q^{88} + 32 q^{91} + 32 q^{92} + 48 q^{93} + 48 q^{95} + 64 q^{97} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1122, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1122, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1122, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(374, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(561, [\chi])\)\(^{\oplus 2}\)