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Properties

Label 1104.6.bc
Level $1104$
Weight $6$
Character orbit 1104.bc
Rep. character $\chi_{1104}(17,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2380$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1104.bc (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1104, [\chi])\).

Total New Old
Modular forms 9720 2420 7300
Cusp forms 9480 2380 7100
Eisenstein series 240 40 200

Trace form

\( 2380 q + 9 q^{3} + 22 q^{7} - 9 q^{9} + O(q^{10}) \) \( 2380 q + 9 q^{3} + 22 q^{7} - 9 q^{9} - 18 q^{13} + 11 q^{15} + 22 q^{19} - 11 q^{21} - 143768 q^{25} + 6183 q^{27} - 7142 q^{31} - 11 q^{33} - 22 q^{37} - 11703 q^{39} + 22 q^{43} + 542608 q^{49} + 11 q^{51} + 2902 q^{55} - 11 q^{57} - 22 q^{61} + 11 q^{63} + 22 q^{67} + 20919 q^{69} - 18 q^{73} + 725567 q^{75} + 22 q^{79} + 602039 q^{81} + 244418 q^{85} + 553899 q^{87} + 1054362 q^{93} - 22 q^{97} - 1011967 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1104, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1104, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1104, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)