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Properties

Label 1122.2.x
Level $1122$
Weight $2$
Character orbit 1122.x
Rep. character $\chi_{1122}(35,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $256$
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 896 256 640
Cusp forms 832 256 576
Eisenstein series 64 0 64

Trace form

\( 256 q - 4 q^{3} - 64 q^{4} + 4 q^{9} + O(q^{10}) \) \( 256 q - 4 q^{3} - 64 q^{4} + 4 q^{9} + 16 q^{12} - 64 q^{16} - 4 q^{22} + 84 q^{25} + 20 q^{27} - 20 q^{28} - 60 q^{30} - 12 q^{31} - 76 q^{33} + 4 q^{36} - 24 q^{37} - 60 q^{39} - 20 q^{40} + 20 q^{42} + 32 q^{45} - 4 q^{48} + 72 q^{49} + 20 q^{52} - 24 q^{55} - 80 q^{57} + 100 q^{58} - 40 q^{61} - 80 q^{63} - 64 q^{64} + 92 q^{66} + 88 q^{67} + 12 q^{69} + 68 q^{70} + 20 q^{72} - 20 q^{73} + 108 q^{75} - 32 q^{78} + 72 q^{81} + 16 q^{82} + 20 q^{84} - 4 q^{88} - 20 q^{90} + 96 q^{91} + 40 q^{93} - 160 q^{94} - 16 q^{97} + 20 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1122, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(561, [\chi])\)\(^{\oplus 2}\)