Properties

Label 966.2.g
Level $966$
Weight $2$
Character orbit 966.g
Rep. character $\chi_{966}(643,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $5$
Sturm bound $384$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(966, [\chi])\).

Total New Old
Modular forms 200 32 168
Cusp forms 184 32 152
Eisenstein series 16 0 16

Trace form

\( 32q + 32q^{4} - 32q^{9} + O(q^{10}) \) \( 32q + 32q^{4} - 32q^{9} + 32q^{16} + 40q^{25} + 32q^{29} - 16q^{35} - 32q^{36} - 16q^{46} + 32q^{50} + 8q^{58} + 32q^{64} - 16q^{70} - 64q^{71} + 48q^{77} - 8q^{78} + 32q^{81} + 80q^{85} + 8q^{93} + 80q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(966, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
966.2.g.a \(4\) \(7.714\) \(\Q(i, \sqrt{14})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
966.2.g.b \(4\) \(7.714\) \(\Q(i, \sqrt{14})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
966.2.g.c \(4\) \(7.714\) \(\Q(i, \sqrt{7})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{3}q^{7}+\cdots\)
966.2.g.d \(4\) \(7.714\) \(\Q(i, \sqrt{7})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
966.2.g.e \(16\) \(7.714\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(966, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)