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Properties

Label 1104.2.t
Level $1104$
Weight $2$
Character orbit 1104.t
Rep. character $\chi_{1104}(277,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 392 176 216
Cusp forms 376 176 200
Eisenstein series 16 0 16

Trace form

\( 176 q + 24 q^{8} + O(q^{10}) \) \( 176 q + 24 q^{8} + 24 q^{10} - 16 q^{12} - 32 q^{14} - 32 q^{20} + 8 q^{22} + 24 q^{28} + 16 q^{30} - 48 q^{31} - 40 q^{32} - 40 q^{34} - 48 q^{35} + 56 q^{38} + 32 q^{43} + 88 q^{44} - 176 q^{49} - 24 q^{50} - 8 q^{52} + 56 q^{56} + 56 q^{58} - 64 q^{59} - 48 q^{60} - 72 q^{64} + 32 q^{65} - 48 q^{66} + 48 q^{67} - 56 q^{68} + 8 q^{70} - 48 q^{74} - 32 q^{75} + 24 q^{76} + 24 q^{78} + 64 q^{80} - 176 q^{81} + 40 q^{82} + 32 q^{86} - 72 q^{88} + 16 q^{90} + 16 q^{91} - 80 q^{94} + 96 q^{95} + 40 q^{96} + 8 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1104, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)