Properties

Label 1148.2.bn
Level $1148$
Weight $2$
Character orbit 1148.bn
Rep. character $\chi_{1148}(169,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $176$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.bn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1148, [\chi])\).

Total New Old
Modular forms 1392 176 1216
Cusp forms 1296 176 1120
Eisenstein series 96 0 96

Trace form

\( 176q + 4q^{3} + O(q^{10}) \) \( 176q + 4q^{3} - 4q^{13} - 32q^{15} + 8q^{17} + 56q^{19} - 12q^{23} + 68q^{25} - 20q^{27} + 20q^{31} - 4q^{35} - 16q^{37} + 80q^{39} + 16q^{41} + 48q^{45} + 8q^{47} - 8q^{51} + 72q^{55} + 8q^{63} + 4q^{65} - 12q^{67} - 68q^{69} - 68q^{71} + 56q^{75} - 140q^{79} - 264q^{81} + 104q^{83} - 96q^{85} - 160q^{87} + 12q^{89} - 16q^{93} - 184q^{95} - 100q^{97} - 128q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1148, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)