Properties

Label 1148.2.w
Level $1148$
Weight $2$
Character orbit 1148.w
Rep. character $\chi_{1148}(489,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $112$
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.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 696 112 584
Cusp forms 648 112 536
Eisenstein series 48 0 48

Trace form

\( 112q - 16q^{9} + O(q^{10}) \) \( 112q - 16q^{9} - 24q^{15} - 4q^{21} - 8q^{29} + 48q^{37} + 8q^{43} - 24q^{49} + 48q^{51} + 112q^{57} + 8q^{63} + 56q^{65} - 16q^{67} + 32q^{71} + 4q^{77} + 8q^{79} - 16q^{85} - 84q^{91} - 32q^{93} + 48q^{95} - 16q^{99} + O(q^{100}) \)

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

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