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Properties

Label 1122.2.bn
Level $1122$
Weight $2$
Character orbit 1122.bn
Rep. character $\chi_{1122}(5,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $2304$
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.bn (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 561 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 7168 2304 4864
Cusp forms 6656 2304 4352
Eisenstein series 512 0 512

Trace form

\( 2304 q + O(q^{10}) \) \( 2304 q + 16 q^{12} + 64 q^{18} - 24 q^{24} + 64 q^{31} + 32 q^{37} - 64 q^{39} + 32 q^{43} - 128 q^{49} + 96 q^{52} - 112 q^{54} - 64 q^{55} + 16 q^{57} - 64 q^{60} - 64 q^{61} + 144 q^{63} - 8 q^{66} + 64 q^{69} + 64 q^{70} + 256 q^{73} + 16 q^{81} - 64 q^{85} + 32 q^{88} - 640 q^{91} - 64 q^{93} + 128 q^{97} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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