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Properties

Label 1148.2.bm
Level $1148$
Weight $2$
Character orbit 1148.bm
Rep. character $\chi_{1148}(251,\cdot)$
Character field $\Q(\zeta_{20})$
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.bm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
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 1376 1376 0
Cusp forms 1312 1312 0
Eisenstein series 64 64 0

Trace form

\( 1312 q - 20 q^{2} - 12 q^{4} - 20 q^{8} + O(q^{10}) \) \( 1312 q - 20 q^{2} - 12 q^{4} - 20 q^{8} + 2 q^{14} - 12 q^{16} + 12 q^{18} - 20 q^{21} + 16 q^{22} - 320 q^{25} + 30 q^{28} + 32 q^{29} + 44 q^{30} + 60 q^{36} - 24 q^{37} + 16 q^{42} - 32 q^{44} - 220 q^{46} - 20 q^{49} - 32 q^{53} + 162 q^{56} - 24 q^{57} + 4 q^{58} - 60 q^{60} - 36 q^{64} + 24 q^{65} - 44 q^{70} + 176 q^{72} - 20 q^{74} - 20 q^{77} + 64 q^{78} - 1280 q^{81} - 10 q^{84} - 8 q^{85} + 4 q^{86} - 76 q^{88} - 124 q^{92} + 8 q^{93} - 16 q^{98} + O(q^{100}) \)

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.