Properties

Label 1104.2.u
Level $1104$
Weight $2$
Character orbit 1104.u
Rep. character $\chi_{1104}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $352$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1104.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1104, [\chi])\).

Total New Old
Modular forms 392 352 40
Cusp forms 376 352 24
Eisenstein series 16 0 16

Trace form

\( 352q + 6q^{6} + O(q^{10}) \) \( 352q + 6q^{6} + 6q^{12} - 20q^{18} - 40q^{22} - 52q^{24} - 12q^{27} - 24q^{28} - 68q^{30} - 34q^{36} - 24q^{39} - 20q^{42} - 32q^{43} + 352q^{49} - 40q^{51} - 8q^{52} + 100q^{54} - 64q^{55} - 36q^{58} + 44q^{60} - 84q^{64} - 92q^{66} - 144q^{70} - 60q^{72} + 56q^{75} - 96q^{76} - 70q^{78} + 4q^{82} - 64q^{84} + 112q^{87} + 152q^{88} + 12q^{90} + 48q^{91} - 24q^{93} - 24q^{94} + 40q^{96} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1104, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1104, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1104, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)