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Properties

Label 1122.2.j
Level $1122$
Weight $2$
Character orbit 1122.j
Rep. character $\chi_{1122}(395,\cdot)$
Character field $\Q(\zeta_{4})$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 561 \)
Character field: \(\Q(i)\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 448 144 304
Cusp forms 416 144 272
Eisenstein series 32 0 32

Trace form

\( 144 q + 4 q^{3} - 144 q^{4} + O(q^{10}) \) \( 144 q + 4 q^{3} - 144 q^{4} - 4 q^{12} + 144 q^{16} + 20 q^{22} - 20 q^{27} + 36 q^{33} + 32 q^{34} + 8 q^{37} + 4 q^{48} + 32 q^{55} - 8 q^{58} - 144 q^{64} + 48 q^{67} - 16 q^{69} + 28 q^{75} - 16 q^{78} - 40 q^{81} + 16 q^{82} - 20 q^{88} + 112 q^{91} - 64 q^{97} + 52 q^{99} + O(q^{100}) \)

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

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