Space of modular forms of level 832, weight 6, and trivial character

• Label: 832.6.a
• Level: $832$
• Weight: $6$
• Character orbit: 832.a
• Rep. character: $\chi_{832}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $34$
• Sturm bound: $672$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	832.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 34 \)
Sturm bound:			\(672\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(832))\).

	Total	New	Old
Modular forms	572	120	452
Cusp forms	548	120	428
Eisenstein series	24	0	24

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

\(2\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(29\)
\(+\)	\(-\)	\(-\)	\(31\)
\(-\)	\(+\)	\(-\)	\(31\)
\(-\)	\(-\)	\(+\)	\(29\)
Plus space		\(+\)	\(58\)
Minus space		\(-\)	\(62\)

Trace form

\( 120 q + 9720 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(832))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	13
832.6.a.a	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				104.6.a.a	$1$	$1$	\(0\)	\(-23\)	\(9\)	\(-165\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-23q^{3}+9q^{5}-165q^{7}+286q^{9}+\cdots\)
832.6.a.b	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				52.6.a.b	$1$	$1$	\(0\)	\(-17\)	\(91\)	\(-233\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-17q^{3}+91q^{5}-233q^{7}+46q^{9}+\cdots\)
832.6.a.c	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				52.6.a.a	$1$	$2$	\(0\)	\(-5\)	\(3\)	\(-53\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}+3q^{5}-53q^{7}-218q^{9}-702q^{11}+\cdots\)
832.6.a.d	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				26.6.a.a	$1$	$0$	\(0\)	\(0\)	\(14\)	\(-170\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+14q^{5}-170q^{7}-3^{5}q^{9}+250q^{11}+\cdots\)
832.6.a.e	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				26.6.a.a	$1$	$1$	\(0\)	\(0\)	\(14\)	\(170\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+14q^{5}+170q^{7}-3^{5}q^{9}-250q^{11}+\cdots\)
832.6.a.f	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				52.6.a.a	$1$	$1$	\(0\)	\(5\)	\(3\)	\(53\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}+3q^{5}+53q^{7}-218q^{9}+702q^{11}+\cdots\)
832.6.a.g	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				52.6.a.b	$1$	$0$	\(0\)	\(17\)	\(91\)	\(233\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+17q^{3}+91q^{5}+233q^{7}+46q^{9}+\cdots\)
832.6.a.h	$832$	$6$	832.a	1.a	$1$	$1$	$1$	$133.439$	\(\Q\)	None	✓				104.6.a.a	$1$	$0$	\(0\)	\(23\)	\(9\)	\(165\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+23q^{3}+9q^{5}+165q^{7}+286q^{9}+\cdots\)
832.6.a.i	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{17}) \)	None	✓				13.6.a.a	$1$	$1$	\(0\)	\(-28\)	\(42\)	\(36\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-14-3\beta )q^{3}+(21-20\beta )q^{5}+(18+\cdots)q^{7}+\cdots\)
832.6.a.j	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{337}) \)	None	✓				104.6.a.b	$1$	$0$	\(0\)	\(-23\)	\(47\)	\(-95\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-11-\beta )q^{3}+(21+5\beta )q^{5}+(-7^{2}+\cdots)q^{7}+\cdots\)
832.6.a.k	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{849}) \)	None	✓				26.6.a.c	$1$	$0$	\(0\)	\(-9\)	\(-73\)	\(155\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-4-\beta )q^{3}+(-38+3\beta )q^{5}+(82+\cdots)q^{7}+\cdots\)
832.6.a.l	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{2785}) \)	None	✓				26.6.a.b	$1$	$1$	\(0\)	\(-9\)	\(37\)	\(327\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-4-\beta )q^{3}+(18+\beta )q^{5}+(164-\beta )q^{7}+\cdots\)
832.6.a.m	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{849}) \)	None	✓				26.6.a.c	$1$	$1$	\(0\)	\(9\)	\(-73\)	\(-155\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(5-\beta )q^{3}+(-35-3\beta )q^{5}+(-73+\cdots)q^{7}+\cdots\)
832.6.a.n	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{2785}) \)	None	✓				26.6.a.b	$1$	$0$	\(0\)	\(9\)	\(37\)	\(-327\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(5-\beta )q^{3}+(19-\beta )q^{5}+(-163-\beta )q^{7}+\cdots\)
832.6.a.o	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{337}) \)	None	✓				104.6.a.b	$1$	$1$	\(0\)	\(23\)	\(47\)	\(95\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(12-\beta )q^{3}+(26-5\beta )q^{5}+(46+3\beta )q^{7}+\cdots\)
832.6.a.p	$832$	$6$	832.a	1.a	$1$	$2$	$2$	$133.439$	\(\Q(\sqrt{17}) \)	None	✓				13.6.a.a	$1$	$0$	\(0\)	\(28\)	\(42\)	\(-36\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(14-3\beta )q^{3}+(21+20\beta )q^{5}+(-18+\cdots)q^{7}+\cdots\)
832.6.a.q	$832$	$6$	832.a	1.a	$1$	$3$	$3$	$133.439$	3.3.1848689.1	None	✓				104.6.a.c	$1$	$0$	\(0\)	\(-20\)	\(-56\)	\(76\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-7+\beta _{1})q^{3}+(-19-\beta _{2})q^{5}+(5^{2}+\cdots)q^{7}+\cdots\)
832.6.a.r	$832$	$6$	832.a	1.a	$1$	$3$	$3$	$133.439$	3.3.203961.1	None	✓				52.6.a.c	$1$	$0$	\(0\)	\(-12\)	\(-8\)	\(138\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-5-2\beta _{1}+\beta _{2})q^{3}+(-6-5\beta _{1}+\cdots)q^{5}+\cdots\)
832.6.a.s	$832$	$6$	832.a	1.a	$1$	$3$	$3$	$133.439$	3.3.168897.1	None	✓				13.6.a.b	$1$	$1$	\(0\)	\(-8\)	\(-56\)	\(-60\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{3}+(-21+4\beta _{1}-3\beta _{2})q^{5}+\cdots\)
832.6.a.t	$832$	$6$	832.a	1.a	$1$	$3$	$3$	$133.439$	3.3.168897.1	None	✓				13.6.a.b	$1$	$0$	\(0\)	\(8\)	\(-56\)	\(60\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{3}+(-21+4\beta _{1}-3\beta _{2})q^{5}+\cdots\)
832.6.a.u	$832$	$6$	832.a	1.a	$1$	$3$	$3$	$133.439$	3.3.203961.1	None	✓				52.6.a.c	$1$	$1$	\(0\)	\(12\)	\(-8\)	\(-138\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(5+2\beta _{1}-\beta _{2})q^{3}+(-6-5\beta _{1}+5\beta _{2})q^{5}+\cdots\)
832.6.a.v	$832$	$6$	832.a	1.a	$1$	$3$	$3$	$133.439$	3.3.1848689.1	None	✓				104.6.a.c	$1$	$1$	\(0\)	\(20\)	\(-56\)	\(-76\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(7-\beta _{1})q^{3}+(-19-\beta _{2})q^{5}+(-5^{2}+\cdots)q^{7}+\cdots\)
832.6.a.w	$832$	$6$	832.a	1.a	$1$	$4$	$4$	$133.439$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				104.6.a.d	$1$	$1$	\(0\)	\(-11\)	\(-31\)	\(-39\)		$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{2})q^{3}+(-7-\beta _{1}-3\beta _{2}+\cdots)q^{5}+\cdots\)
832.6.a.x	$832$	$6$	832.a	1.a	$1$	$4$	$4$	$133.439$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				104.6.a.d	$1$	$0$	\(0\)	\(11\)	\(-31\)	\(39\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{2})q^{3}+(-7-\beta _{1}-3\beta _{2}-\beta _{3})q^{5}+\cdots\)
832.6.a.y	$832$	$6$	832.a	1.a	$1$	$5$	$5$	$133.439$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				104.6.a.e	$1$	$1$	\(0\)	\(-9\)	\(-19\)	\(-109\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(-4+\beta _{1}-\beta _{3})q^{5}+\cdots\)
832.6.a.z	$832$	$6$	832.a	1.a	$1$	$5$	$5$	$133.439$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				104.6.a.e	$1$	$0$	\(0\)	\(9\)	\(-19\)	\(109\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+(-4+\beta _{1}-\beta _{3})q^{5}+\cdots\)
832.6.a.ba	$832$	$6$	832.a	1.a	$1$	$6$	$6$	$133.439$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				416.6.a.b	$2$	$1$	\(0\)	\(0\)	\(-112\)	\(0\)		$-$	$-$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-19-\beta _{3})q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
832.6.a.bb	$832$	$6$	832.a	1.a	$1$	$6$	$6$	$133.439$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				416.6.a.a	$2$	$0$	\(0\)	\(0\)	\(112\)	\(0\)		$-$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(19+\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
832.6.a.bc	$832$	$6$	832.a	1.a	$1$	$7$	$7$	$133.439$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				416.6.a.c	$1$	$1$	\(0\)	\(-17\)	\(-25\)	\(147\)		$+$	$+$	$+$	$2^{11}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{3}+(-4-\beta _{2})q^{5}+(21+\cdots)q^{7}+\cdots\)
832.6.a.bd	$832$	$6$	832.a	1.a	$1$	$7$	$7$	$133.439$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				416.6.a.c	$1$	$1$	\(0\)	\(17\)	\(-25\)	\(-147\)		$+$	$+$	$+$	$2^{11}$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{3}+(-4-\beta _{2})q^{5}+(-21+\cdots)q^{7}+\cdots\)
832.6.a.be	$832$	$6$	832.a	1.a	$1$	$8$	$8$	$133.439$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				416.6.a.e	$1$	$0$	\(0\)	\(-1\)	\(75\)	\(147\)		$+$	$-$	$-$	$2^{16}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(9+\beta _{3})q^{5}+(19-\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
832.6.a.bf	$832$	$6$	832.a	1.a	$1$	$8$	$8$	$133.439$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		416.6.a.f	$2$	$1$	\(0\)	\(0\)	\(-38\)	\(0\)		$-$	$-$	$+$	$2^{17}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-5+\beta _{3})q^{5}+(-5\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
832.6.a.bg	$832$	$6$	832.a	1.a	$1$	$8$	$8$	$133.439$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				416.6.a.e	$1$	$0$	\(0\)	\(1\)	\(75\)	\(-147\)		$+$	$-$	$-$	$2^{16}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(9+\beta _{3})q^{5}+(-19+\beta _{1}+\cdots)q^{7}+\cdots\)
832.6.a.bh	$832$	$6$	832.a	1.a	$1$	$10$	$10$	$133.439$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		416.6.a.h	$2$	$0$	\(0\)	\(0\)	\(-62\)	\(0\)		$-$	$+$	$-$	$2^{26}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-6-\beta _{2})q^{5}-\beta _{6}q^{7}+(133+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(832))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(832)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 2}\)