Properties

Label 966.2.f
Level $966$
Weight $2$
Character orbit 966.f
Rep. character $\chi_{966}(461,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $3$
Sturm bound $384$
Trace bound $1$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 200 56 144
Cusp forms 184 56 128
Eisenstein series 16 0 16

Trace form

\( 56q - 56q^{4} + 8q^{7} - 8q^{9} + O(q^{10}) \) \( 56q - 56q^{4} + 8q^{7} - 8q^{9} + 16q^{15} + 56q^{16} - 12q^{21} + 8q^{22} + 48q^{25} - 8q^{28} + 24q^{30} + 8q^{36} + 40q^{37} + 40q^{39} + 28q^{42} + 40q^{43} - 24q^{49} - 8q^{51} - 56q^{57} - 56q^{58} - 16q^{60} + 24q^{63} - 56q^{64} - 88q^{67} - 32q^{70} - 16q^{78} + 48q^{79} + 8q^{81} + 12q^{84} + 64q^{85} - 8q^{88} - 8q^{91} - 16q^{93} + 64q^{99} + O(q^{100}) \)

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.f.a \(4\) \(7.714\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}-q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
966.2.f.b \(24\) \(7.714\) None \(0\) \(0\) \(0\) \(-4\)
966.2.f.c \(28\) \(7.714\) None \(0\) \(0\) \(0\) \(4\)

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)