Properties

Label 966.2.i
Level $966$
Weight $2$
Character orbit 966.i
Rep. character $\chi_{966}(277,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $14$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(384\)
Trace bound: \(5\)
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 400 56 344
Cusp forms 368 56 312
Eisenstein series 32 0 32

Trace form

\( 56 q - 28 q^{4} + 8 q^{6} - 4 q^{7} - 28 q^{9} + O(q^{10}) \) \( 56 q - 28 q^{4} + 8 q^{6} - 4 q^{7} - 28 q^{9} + 4 q^{10} + 16 q^{13} - 8 q^{14} - 8 q^{15} - 28 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 24 q^{22} - 4 q^{24} - 16 q^{25} - 4 q^{28} - 32 q^{29} - 4 q^{31} + 4 q^{33} + 40 q^{35} + 56 q^{36} + 8 q^{37} + 8 q^{38} - 8 q^{39} + 4 q^{40} - 16 q^{41} - 4 q^{42} + 32 q^{43} - 32 q^{47} - 44 q^{49} + 64 q^{50} - 8 q^{52} - 8 q^{53} - 4 q^{54} - 40 q^{55} - 8 q^{56} + 32 q^{57} - 28 q^{58} - 24 q^{59} + 4 q^{60} + 16 q^{61} + 32 q^{62} + 8 q^{63} + 56 q^{64} - 40 q^{65} - 32 q^{67} + 8 q^{68} + 16 q^{69} - 4 q^{70} + 80 q^{71} - 16 q^{73} - 32 q^{74} - 16 q^{76} + 48 q^{77} - 16 q^{78} + 4 q^{79} - 28 q^{81} - 80 q^{83} + 16 q^{84} + 96 q^{85} + 4 q^{87} + 12 q^{88} - 16 q^{89} - 8 q^{90} + 120 q^{91} - 16 q^{94} - 16 q^{95} - 4 q^{96} - 88 q^{97} - 16 q^{98} + O(q^{100}) \)

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.i.a \(2\) \(7.714\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-4\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.b \(2\) \(7.714\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.c \(2\) \(7.714\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.d \(2\) \(7.714\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(3\) \(-5\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.e \(2\) \(7.714\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.f \(2\) \(7.714\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.g \(2\) \(7.714\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(3\) \(5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.h \(4\) \(7.714\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(2\) \(-2\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
966.2.i.i \(4\) \(7.714\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(-2\) \(1\) \(2\) \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
966.2.i.j \(4\) \(7.714\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(2\) \(-2\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
966.2.i.k \(6\) \(7.714\) 6.0.29428272.1 None \(3\) \(3\) \(-3\) \(-3\) \(q+(1+\beta _{3})q^{2}-\beta _{3}q^{3}+\beta _{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
966.2.i.l \(8\) \(7.714\) 8.0.1768034304.4 None \(-4\) \(-4\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
966.2.i.m \(8\) \(7.714\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(4\) \(-2\) \(6\) \(q+(-1-\beta _{1})q^{2}-\beta _{1}q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{5}+\cdots\)
966.2.i.n \(8\) \(7.714\) 8.0.\(\cdots\).2 None \(4\) \(4\) \(-2\) \(0\) \(q+(1+\beta _{5})q^{2}-\beta _{5}q^{3}+\beta _{5}q^{4}-\beta _{1}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)