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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

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

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

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