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Properties

Label 966.4.a
Level $966$
Weight $4$
Character orbit 966.a
Rep. character $\chi_{966}(1,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $18$
Sturm bound $768$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(768\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(966))\).

Total New Old
Modular forms 584 68 516
Cusp forms 568 68 500
Eisenstein series 16 0 16

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(5\)
\(+\)\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(+\)\(-\)\(-\)$+$\(4\)
\(+\)\(-\)\(+\)\(+\)$-$\(4\)
\(+\)\(-\)\(+\)\(-\)$+$\(5\)
\(+\)\(-\)\(-\)\(+\)$+$\(6\)
\(+\)\(-\)\(-\)\(-\)$-$\(3\)
\(-\)\(+\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(+\)\(-\)$+$\(5\)
\(-\)\(+\)\(-\)\(+\)$+$\(4\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(5\)
\(-\)\(-\)\(+\)\(-\)$-$\(3\)
\(-\)\(-\)\(-\)\(+\)$-$\(2\)
\(-\)\(-\)\(-\)\(-\)$+$\(6\)
Plus space\(+\)\(40\)
Minus space\(-\)\(28\)

Trace form

\( 68 q - 8 q^{2} + 272 q^{4} - 40 q^{5} - 32 q^{8} + 612 q^{9} + O(q^{10}) \) \( 68 q - 8 q^{2} + 272 q^{4} - 40 q^{5} - 32 q^{8} + 612 q^{9} - 80 q^{10} - 104 q^{13} + 1088 q^{16} - 136 q^{17} - 72 q^{18} - 160 q^{20} + 1700 q^{25} + 144 q^{26} - 24 q^{29} + 480 q^{31} - 128 q^{32} + 384 q^{33} - 304 q^{34} + 2448 q^{36} - 104 q^{37} - 320 q^{40} - 56 q^{41} + 448 q^{43} - 360 q^{45} + 368 q^{46} + 1040 q^{47} + 3332 q^{49} - 856 q^{50} - 480 q^{51} - 416 q^{52} + 2136 q^{53} + 4240 q^{55} + 1536 q^{57} + 2512 q^{59} - 1944 q^{61} + 704 q^{62} + 4352 q^{64} + 1776 q^{65} + 2928 q^{67} - 544 q^{68} + 560 q^{70} + 1280 q^{71} - 288 q^{72} - 2504 q^{73} - 1456 q^{74} - 192 q^{75} + 896 q^{77} + 624 q^{78} + 1888 q^{79} - 640 q^{80} + 5508 q^{81} - 592 q^{82} + 464 q^{83} + 2624 q^{85} + 2976 q^{86} - 1392 q^{87} + 2024 q^{89} - 720 q^{90} + 744 q^{93} + 2976 q^{94} - 3872 q^{95} - 3832 q^{97} - 392 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(966))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 23
966.4.a.a 966.a 1.a $1$ $56.996$ \(\Q\) None \(-2\) \(3\) \(-6\) \(7\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
966.4.a.b 966.a 1.a $1$ $56.996$ \(\Q\) None \(2\) \(-3\) \(-9\) \(7\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-9q^{5}-6q^{6}+\cdots\)
966.4.a.c 966.a 1.a $2$ $56.996$ \(\Q(\sqrt{13}) \) None \(4\) \(6\) \(-15\) \(14\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-7-\beta )q^{5}+\cdots\)
966.4.a.d 966.a 1.a $3$ $56.996$ 3.3.29901.1 None \(-6\) \(9\) \(-5\) \(21\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
966.4.a.e 966.a 1.a $3$ $56.996$ 3.3.65101.1 None \(6\) \(-9\) \(5\) \(-21\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(2+\beta _{2})q^{5}+\cdots\)
966.4.a.f 966.a 1.a $3$ $56.996$ 3.3.12197.1 None \(6\) \(-9\) \(9\) \(21\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(4-3\beta _{1})q^{5}+\cdots\)
966.4.a.g 966.a 1.a $3$ $56.996$ 3.3.2981.1 None \(6\) \(9\) \(-15\) \(-21\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-4-3\beta _{1}+\cdots)q^{5}+\cdots\)
966.4.a.h 966.a 1.a $4$ $56.996$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(-5\) \(-28\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
966.4.a.i 966.a 1.a $4$ $56.996$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(10\) \(28\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(2+\beta _{1})q^{5}+\cdots\)
966.4.a.j 966.a 1.a $4$ $56.996$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(12\) \(5\) \(-28\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(1-\beta _{2})q^{5}+\cdots\)
966.4.a.k 966.a 1.a $4$ $56.996$ 4.4.9814581.1 None \(8\) \(-12\) \(-15\) \(28\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-3-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
966.4.a.l 966.a 1.a $5$ $56.996$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-15\) \(-15\) \(35\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-3+\beta _{2})q^{5}+\cdots\)
966.4.a.m 966.a 1.a $5$ $56.996$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-15\) \(10\) \(-35\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1})q^{5}+\cdots\)
966.4.a.n 966.a 1.a $5$ $56.996$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(15\) \(0\) \(-35\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+\beta _{2}q^{5}-6q^{6}+\cdots\)
966.4.a.o 966.a 1.a $5$ $56.996$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(15\) \(6\) \(35\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(1+\beta _{1})q^{5}+\cdots\)
966.4.a.p 966.a 1.a $5$ $56.996$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-15\) \(-10\) \(-35\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
966.4.a.q 966.a 1.a $5$ $56.996$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(15\) \(-10\) \(-35\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-2-\beta _{1})q^{5}+\cdots\)
966.4.a.r 966.a 1.a $6$ $56.996$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(18\) \(20\) \(42\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(966))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(966)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 2}\)