Properties

Label 1148.1.o
Level $1148$
Weight $1$
Character orbit 1148.o
Rep. character $\chi_{1148}(163,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $4$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1148.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(168\)
Trace bound: \(3\)

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 16 16 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q - 8q^{4} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{4} - 8q^{9} - 8q^{16} - 8q^{25} + 16q^{36} + 16q^{41} - 8q^{42} + 8q^{45} - 16q^{50} - 16q^{57} + 16q^{64} + 8q^{66} - 8q^{77} - 8q^{81} + 32q^{90} + O(q^{100}) \)

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.o.a \(2\) \(0.573\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-41}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1148.1.o.b \(2\) \(0.573\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-41}) \) None \(-1\) \(1\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1148.1.o.c \(4\) \(0.573\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{4}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1148.1.o.d \(8\) \(0.573\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-41}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\cdots\)