Properties

Label 1122.2.z
Level $1122$
Weight $2$
Character orbit 1122.z
Rep. character $\chi_{1122}(109,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $288$
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.z (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 1792 288 1504
Cusp forms 1664 288 1376
Eisenstein series 128 0 128

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 32 q^{11} + 64 q^{14} + 32 q^{22} - 64 q^{23} + 64 q^{25} - 64 q^{31} + 32 q^{37} + 128 q^{49} - 32 q^{55} + 64 q^{59} + 64 q^{69} - 64 q^{70} + 128 q^{75} - 96 q^{77} + 64 q^{80} + 128 q^{86} - 32 q^{88} + 64 q^{91} - 64 q^{92} + 128 q^{97} - 32 q^{99} + O(q^{100}) \)

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

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