Properties

Label 1216.1.e
Level $1216$
Weight $1$
Character orbit 1216.e
Rep. character $\chi_{1216}(1025,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $160$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1216.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 22 4 18
Cusp forms 10 2 8
Eisenstein series 12 2 10

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + 2q^{5} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{5} + 2q^{9} - 2q^{17} + 2q^{45} + 2q^{61} - 2q^{73} - 2q^{77} + 2q^{81} - 2q^{85} + O(q^{100}) \)

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.e.a \(1\) \(0.607\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+q^{5}-q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
1216.1.e.b \(1\) \(0.607\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)