Properties

Label 1148.1.bc
Level $1148$
Weight $1$
Character orbit 1148.bc
Rep. character $\chi_{1148}(461,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1148.bc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1148, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 8 8 0
Eisenstein series 24 0 24

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 0 8

Trace form

\( 8q - 2q^{7} + O(q^{10}) \) \( 8q - 2q^{7} + 4q^{11} - 2q^{15} - 4q^{23} - 6q^{29} - 2q^{37} - 2q^{39} - 2q^{43} - 2q^{49} - 4q^{51} - 2q^{57} + 2q^{65} + 4q^{77} + 8q^{79} - 8q^{81} + 4q^{85} + 6q^{93} + 2q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1148.1.bc.a \(8\) \(0.573\) \(\Q(\zeta_{20})\) \(A_{5}\) None None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{20}^{5}q^{3}-\zeta_{20}q^{5}-\zeta_{20}^{2}q^{7}+(\zeta_{20}^{2}+\cdots)q^{11}+\cdots\)