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Properties

Label 1148.2.bk
Level $1148$
Weight $2$
Character orbit 1148.bk
Rep. character $\chi_{1148}(37,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $224$
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.bk (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1392 224 1168
Cusp forms 1296 224 1072
Eisenstein series 96 0 96

Trace form

\( 224 q + 4 q^{5} - 116 q^{9} + O(q^{10}) \) \( 224 q + 4 q^{5} - 116 q^{9} - 4 q^{11} - 12 q^{15} + 6 q^{17} - 4 q^{19} + 17 q^{21} - 3 q^{23} + 32 q^{25} + 12 q^{27} + 8 q^{29} + 4 q^{31} + 11 q^{33} - 24 q^{35} + 11 q^{37} + 10 q^{39} + 34 q^{41} - 28 q^{43} - 14 q^{45} + 22 q^{47} + 56 q^{49} - q^{51} - 7 q^{53} - 28 q^{55} + 44 q^{57} - 14 q^{59} + 54 q^{61} + 18 q^{63} + 31 q^{65} + 16 q^{67} - 96 q^{69} + 66 q^{71} - 26 q^{73} + 39 q^{75} - 92 q^{77} + 10 q^{79} - 80 q^{81} + 48 q^{83} - 72 q^{85} - 22 q^{87} + 18 q^{89} + 14 q^{91} - 40 q^{93} + 6 q^{95} - 12 q^{97} - 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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