Properties

Label 1148.2.cf
Level $1148$
Weight $2$
Character orbit 1148.cf
Rep. character $\chi_{1148}(121,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $448$
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.cf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 2784 448 2336
Cusp forms 2592 448 2144
Eisenstein series 192 0 192

Trace form

\( 448q + O(q^{10}) \) \( 448q + 4q^{11} - 12q^{15} + 6q^{17} - 4q^{19} - 56q^{25} - 12q^{27} + 32q^{29} - 8q^{31} + 110q^{33} + 24q^{35} - 42q^{37} - 44q^{41} + 40q^{43} + 40q^{45} + 52q^{47} + 20q^{49} - 42q^{51} - 26q^{53} - 4q^{55} - 40q^{57} - 12q^{59} - 80q^{61} + 34q^{63} + 12q^{65} + 20q^{67} - 12q^{69} + 4q^{71} + 90q^{75} + 20q^{77} + 18q^{79} + 216q^{81} - 208q^{83} - 72q^{85} + 22q^{89} + 100q^{93} + 8q^{95} - 52q^{97} - 80q^{99} + O(q^{100}) \)

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

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