Properties

Label 1216.2.b
Level $1216$
Weight $2$
Character orbit 1216.b
Rep. character $\chi_{1216}(607,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $6$
Sturm bound $320$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(320\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1216, [\chi])\).

Total New Old
Modular forms 172 40 132
Cusp forms 148 40 108
Eisenstein series 24 0 24

Trace form

\( 40q - 40q^{9} + O(q^{10}) \) \( 40q - 40q^{9} - 40q^{25} - 72q^{49} + 8q^{57} - 32q^{73} + 88q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1216.2.b.a \(4\) \(9.710\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-q^{9}+\cdots\)
1216.2.b.b \(4\) \(9.710\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-q^{9}+\cdots\)
1216.2.b.c \(4\) \(9.710\) \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-3\beta _{1}q^{7}+3q^{9}+\beta _{2}q^{11}+\cdots\)
1216.2.b.d \(8\) \(9.710\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-4q^{9}-\beta _{7}q^{13}+\cdots\)
1216.2.b.e \(8\) \(9.710\) 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{6}q^{7}+3q^{9}+(-2\beta _{1}+\beta _{5}+\cdots)q^{11}+\cdots\)
1216.2.b.f \(12\) \(9.710\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) \(\Q(\sqrt{-38}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{7}q^{7}+(-3+\beta _{2})q^{9}+\beta _{5}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

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