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Properties

Label 1122.2.w
Level $1122$
Weight $2$
Character orbit 1122.w
Rep. character $\chi_{1122}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
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.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
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 896 144 752
Cusp forms 832 144 688
Eisenstein series 64 0 64

Trace form

\( 144 q - 36 q^{4} + 36 q^{9} + O(q^{10}) \) \( 144 q - 36 q^{4} + 36 q^{9} - 8 q^{13} - 8 q^{15} - 36 q^{16} - 8 q^{17} - 16 q^{19} - 32 q^{21} + 88 q^{25} - 8 q^{30} - 4 q^{33} - 8 q^{34} + 40 q^{35} + 36 q^{36} - 16 q^{38} + 8 q^{42} + 64 q^{43} + 16 q^{47} + 44 q^{49} + 32 q^{51} + 12 q^{52} - 8 q^{53} + 80 q^{55} + 8 q^{59} + 12 q^{60} - 36 q^{64} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 52 q^{69} + 32 q^{70} + 24 q^{76} + 88 q^{77} - 36 q^{81} + 48 q^{83} + 8 q^{84} - 88 q^{85} + 16 q^{86} - 24 q^{87} - 64 q^{89} - 24 q^{93} - 40 q^{94} - 64 q^{98} + O(q^{100}) \)

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

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