Properties

Label 1216.2.t
Level $1216$
Weight $2$
Character orbit 1216.t
Rep. character $\chi_{1216}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $5$
Sturm bound $320$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(320\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 344 80 264
Cusp forms 296 80 216
Eisenstein series 48 0 48

Trace form

\( 80q + 40q^{9} + O(q^{10}) \) \( 80q + 40q^{9} + 40q^{25} - 48q^{33} - 24q^{41} + 112q^{49} + 8q^{57} + 16q^{73} - 16q^{81} + 32q^{97} + O(q^{100}) \)

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.t.a \(8\) \(9.710\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{3})q^{3}+(4\zeta_{24}^{2}-\zeta_{24}^{7})q^{9}+\cdots\)
1216.2.t.b \(8\) \(9.710\) 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) \(q+(3\beta _{1}-3\beta _{3})q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+\cdots\)
1216.2.t.c \(16\) \(9.710\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{3}-\beta _{7}q^{5}-\beta _{11}q^{7}+2\beta _{1}q^{9}+\cdots\)
1216.2.t.d \(24\) \(9.710\) None \(0\) \(0\) \(-6\) \(0\)
1216.2.t.e \(24\) \(9.710\) None \(0\) \(0\) \(6\) \(0\)

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

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