Properties

Label 1104.2.bc
Level $1104$
Weight $2$
Character orbit 1104.bc
Rep. character $\chi_{1104}(17,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $460$
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.bc (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 2040 500 1540
Cusp forms 1800 460 1340
Eisenstein series 240 40 200

Trace form

\( 460q + 9q^{3} + 22q^{7} - 9q^{9} + O(q^{10}) \) \( 460q + 9q^{3} + 22q^{7} - 9q^{9} - 18q^{13} + 11q^{15} + 22q^{19} - 11q^{21} - 56q^{25} - 9q^{27} + 26q^{31} - 11q^{33} - 22q^{37} + 9q^{39} + 22q^{43} + 16q^{49} + 11q^{51} + 22q^{55} - 11q^{57} - 22q^{61} + 11q^{63} + 22q^{67} - 9q^{69} - 18q^{73} + 47q^{75} + 22q^{79} - 73q^{81} + 2q^{85} + 171q^{87} + 90q^{93} - 22q^{97} + 209q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1104, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)