Space of modular forms of level 464, weight 6, and trivial character

• Label: 464.6.a
• Level: $464$
• Weight: $6$
• Character orbit: 464.a
• Rep. character: $\chi_{464}(1,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $15$
• Sturm bound: $360$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	464.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(360\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(464))\).

	Total	New	Old
Modular forms	306	70	236
Cusp forms	294	70	224
Eisenstein series	12	0	12

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

\(2\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(16\)
\(+\)	\(-\)	$-$	\(19\)
\(-\)	\(+\)	$-$	\(19\)
\(-\)	\(-\)	$+$	\(16\)
Plus space		\(+\)	\(32\)
Minus space		\(-\)	\(38\)

Trace form

\( 70 q + 18 q^{3} - 124 q^{7} + 5714 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(464))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	29
464.6.a.a	$464$	$6$	464.a	1.a	$1$	$1$	$1$	$74.418$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-16\)	\(54\)	\(-112\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{3}+54q^{5}-112q^{7}+13q^{9}+\cdots\)
464.6.a.b	$464$	$6$	464.a	1.a	$1$	$1$	$1$	$74.418$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(23\)	\(-67\)	\(186\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+23q^{3}-67q^{5}+186q^{7}+286q^{9}+\cdots\)
464.6.a.c	$464$	$6$	464.a	1.a	$1$	$2$	$2$	$74.418$	\(\Q(\sqrt{34}) \)	None	✓	$1$	$1$	\(0\)	\(-34\)	\(-50\)	\(208\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-17+\beta )q^{3}+(-5^{2}+12\beta )q^{5}+\cdots\)
464.6.a.d	$464$	$6$	464.a	1.a	$1$	$2$	$2$	$74.418$	\(\Q(\sqrt{22}) \)	None	✓	$1$	$1$	\(0\)	\(14\)	\(-82\)	\(160\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(7+\beta )q^{3}+(-41+10\beta )q^{5}+(80+\cdots)q^{7}+\cdots\)
464.6.a.e	$464$	$6$	464.a	1.a	$1$	$2$	$2$	$74.418$	\(\Q(\sqrt{202}) \)	None	✓	$1$	$1$	\(0\)	\(22\)	\(-18\)	\(-160\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(11+\beta )q^{3}-9q^{5}+(-80-2\beta )q^{7}+\cdots\)
464.6.a.f	$464$	$6$	464.a	1.a	$1$	$3$	$3$	$74.418$	3.3.431464.1	None	✓	$1$	$1$	\(0\)	\(-14\)	\(68\)	\(-24\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-4-\beta _{1}-\beta _{2})q^{3}+(21+5\beta _{2})q^{5}+\cdots\)
464.6.a.g	$464$	$6$	464.a	1.a	$1$	$4$	$4$	$74.418$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-13\)	\(93\)	\(-134\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{3}+(23-\beta _{2})q^{5}+(-34+\cdots)q^{7}+\cdots\)
464.6.a.h	$464$	$6$	464.a	1.a	$1$	$4$	$4$	$74.418$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(13\)	\(-7\)	\(74\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1}-\beta _{2})q^{3}+(-3+2\beta _{1}-3\beta _{2}+\cdots)q^{5}+\cdots\)
464.6.a.i	$464$	$6$	464.a	1.a	$1$	$4$	$4$	$74.418$	4.4.3257317.1	None	✓	$1$	$0$	\(0\)	\(28\)	\(-68\)	\(208\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(7-\beta _{2})q^{3}+(-17-2\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
464.6.a.j	$464$	$6$	464.a	1.a	$1$	$6$	$6$	$74.418$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-35\)	\(99\)	\(-334\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-6+\beta _{1})q^{3}+(17+\beta _{2})q^{5}+(-57+\cdots)q^{7}+\cdots\)
464.6.a.k	$464$	$6$	464.a	1.a	$1$	$7$	$7$	$74.418$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-26\)	\(32\)	\(-184\)		$-$	$-$	$+$	$2^{13}$	$\mathrm{SU}(2)$	\(q+(-4+\beta _{4})q^{3}+(5-\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
464.6.a.l	$464$	$6$	464.a	1.a	$1$	$8$	$8$	$74.418$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(25\)	\(-282\)		$+$	$+$	$+$	$2^{13}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(3-\beta _{2})q^{5}+(-35-\beta _{3}+\cdots)q^{7}+\cdots\)
464.6.a.m	$464$	$6$	464.a	1.a	$1$	$8$	$8$	$74.418$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(23\)	\(-75\)	\(-74\)		$+$	$+$	$+$	$2^{13}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{3}+(-10+\beta _{1}+\beta _{2})q^{5}+\cdots\)
464.6.a.n	$464$	$6$	464.a	1.a	$1$	$9$	$9$	$74.418$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(12\)	\(46\)	\(136\)		$+$	$-$	$-$	$2^{15}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(5+\beta _{1}+\beta _{2})q^{5}+(15+\cdots)q^{7}+\cdots\)
464.6.a.o	$464$	$6$	464.a	1.a	$1$	$9$	$9$	$74.418$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(24\)	\(-50\)	\(208\)		$+$	$-$	$-$	$2^{15}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{3}+(-6-\beta _{4})q^{5}+(23-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(464))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(464)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 2}\)