Properties

Label 1216.1.g
Level $1216$
Weight $1$
Character orbit 1216.g
Rep. character $\chi_{1216}(417,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $160$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1216.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1216, [\chi])\).

Total New Old
Modular forms 30 6 24
Cusp forms 18 6 12
Eisenstein series 12 0 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{9} - 6q^{25} + 6q^{49} + 6q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1216.1.g.a \(2\) \(0.607\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{38}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-iq^{11}+q^{17}-iq^{19}+q^{25}+\cdots\)
1216.1.g.b \(4\) \(0.607\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)