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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
966.2.g.a 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{14})\) None 966.2.g.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
966.2.g.b 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{14})\) None 966.2.g.b \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
966.2.g.c 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{7})\) None 966.2.g.c \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{3}q^{7}+\cdots\)
966.2.g.d 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{7})\) None 966.2.g.d \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
966.2.g.e 966.g 161.c $16$ $7.714$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 966.2.g.e \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{2}q^{6}+\cdots\)

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

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