Properties

Label 966.2.y
Level $966$
Weight $2$
Character orbit 966.y
Rep. character $\chi_{966}(25,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $640$
Newform subspaces $4$
Sturm bound $384$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.y (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Newform subspaces: \( 4 \)
Sturm bound: \(384\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 4000 640 3360
Cusp forms 3680 640 3040
Eisenstein series 320 0 320

Trace form

\( 640q + 32q^{4} + 8q^{5} - 8q^{7} + 32q^{9} + O(q^{10}) \) \( 640q + 32q^{4} + 8q^{5} - 8q^{7} + 32q^{9} - 8q^{10} + 16q^{11} - 8q^{14} + 32q^{16} - 16q^{17} + 72q^{20} + 16q^{22} + 84q^{23} + 104q^{25} + 8q^{26} - 72q^{28} + 16q^{29} - 8q^{30} + 8q^{31} - 8q^{33} + 16q^{34} + 20q^{35} - 64q^{36} + 44q^{37} + 16q^{38} - 8q^{40} + 16q^{41} + 16q^{42} - 88q^{43} + 16q^{44} + 8q^{45} - 4q^{46} + 8q^{47} + 48q^{49} - 32q^{50} + 52q^{51} - 16q^{53} - 16q^{55} + 16q^{56} - 72q^{57} - 44q^{58} + 96q^{59} + 128q^{61} - 48q^{62} - 8q^{63} - 64q^{64} + 16q^{65} - 16q^{66} + 8q^{67} - 16q^{68} - 24q^{69} + 96q^{70} - 64q^{71} + 40q^{73} + 8q^{74} + 16q^{75} + 8q^{77} - 88q^{79} + 8q^{80} + 32q^{81} + 88q^{82} + 144q^{83} + 8q^{85} + 24q^{86} + 24q^{87} - 8q^{88} + 16q^{89} + 16q^{90} - 80q^{91} + 8q^{92} - 8q^{93} + 16q^{94} + 52q^{95} + 64q^{97} + 56q^{98} + 56q^{99} + O(q^{100}) \)

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.y.a \(160\) \(7.714\) None \(-8\) \(-8\) \(2\) \(-2\)
966.2.y.b \(160\) \(7.714\) None \(-8\) \(8\) \(6\) \(-10\)
966.2.y.c \(160\) \(7.714\) None \(8\) \(-8\) \(2\) \(-2\)
966.2.y.d \(160\) \(7.714\) None \(8\) \(8\) \(-2\) \(6\)

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

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