Properties

Label 1176.1.s
Level $1176$
Weight $1$
Character orbit 1176.s
Rep. character $\chi_{1176}(557,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $3$
Sturm bound $224$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1176.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(224\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1176, [\chi])\).

Total New Old
Modular forms 52 28 24
Cusp forms 20 12 8
Eisenstein series 32 16 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 2 q^{4} - 4 q^{6} - 2 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{4} - 4 q^{6} - 2 q^{9} - 2 q^{10} - 12 q^{15} - 6 q^{16} - 4 q^{18} - 4 q^{22} + 2 q^{24} - 4 q^{25} + 4 q^{30} - 2 q^{31} - 2 q^{33} + 4 q^{36} + 4 q^{39} - 2 q^{40} + 2 q^{54} - 4 q^{55} - 8 q^{57} + 2 q^{58} - 2 q^{60} - 4 q^{64} + 4 q^{72} + 4 q^{73} + 8 q^{78} + 2 q^{79} + 2 q^{81} - 2 q^{87} + 2 q^{88} + 4 q^{90} + 2 q^{96} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1176.1.s.a $2$ $0.587$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)
1176.1.s.b $2$ $0.587$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-6}) \) None \(1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
1176.1.s.c $8$ $0.587$ \(\Q(\zeta_{24})\) $D_{4}$ \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)