Properties

Label 1148.1.bj
Level $1148$
Weight $1$
Character orbit 1148.bj
Rep. character $\chi_{1148}(319,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $8$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1148.bj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{12})\)
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 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

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

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

Trace form

\( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{10} - 8q^{13} - 4q^{16} + 4q^{26} + 4q^{40} - 4q^{42} - 4q^{52} - 4q^{53} + 8q^{57} - 8q^{64} - 4q^{65} + 4q^{66} - 4q^{81} + 4q^{82} - 4q^{89} - 4q^{93} - 8q^{98} + O(q^{100}) \)

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.bj.a \(8\) \(0.573\) \(\Q(\zeta_{24})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)