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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

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

Display 100 coefficients 10 coefficients

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

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