Properties

Label 1148.2.bu
Level $1148$
Weight $2$
Character orbit 1148.bu
Rep. character $\chi_{1148}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1312$
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.bu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1376 1376 0
Cusp forms 1312 1312 0
Eisenstein series 64 64 0

Trace form

\( 1312q - 3q^{2} - 3q^{4} - 18q^{5} - 640q^{9} + O(q^{10}) \) \( 1312q - 3q^{2} - 3q^{4} - 18q^{5} - 640q^{9} + 18q^{10} - 9q^{12} - 18q^{14} - 3q^{16} - 18q^{17} + 14q^{21} - 28q^{22} + 54q^{24} - 154q^{25} + 9q^{26} + 23q^{28} + 21q^{30} - 18q^{32} - 18q^{33} - 70q^{36} - 6q^{37} - 66q^{38} - 54q^{40} + 40q^{42} + 8q^{44} + 60q^{45} + 20q^{46} + 4q^{49} - 48q^{50} - 69q^{52} - 6q^{53} + 111q^{54} + 26q^{56} + 12q^{57} + 15q^{58} - 22q^{60} - 18q^{61} - 120q^{64} - 18q^{65} - 108q^{66} - 210q^{68} + 87q^{70} - 33q^{72} - 48q^{73} + 9q^{74} + 16q^{77} + 58q^{78} - 27q^{80} - 632q^{81} - 207q^{82} + 81q^{84} - 56q^{85} + 9q^{86} - 22q^{88} + 162q^{89} - 62q^{92} + 6q^{93} - 45q^{94} - 180q^{96} - 16q^{98} + O(q^{100}) \)

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

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