Space of modular forms of level 464, weight 8, and trivial character

• Label: 464.8.a
• Level: $464$
• Weight: $8$
• Character orbit: 464.a
• Rep. character: $\chi_{464}(1,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $12$
• Sturm bound: $480$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	464.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(480\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(464))\).

	Total	New	Old
Modular forms	426	98	328
Cusp forms	414	98	316
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
\(+\)	\(+\)	\(+\)	\(26\)
\(+\)	\(-\)	\(-\)	\(23\)
\(-\)	\(+\)	\(-\)	\(23\)
\(-\)	\(-\)	\(+\)	\(26\)
Plus space		\(+\)	\(52\)
Minus space		\(-\)	\(46\)

Trace form

\( 98 q - 54 q^{3} - 2012 q^{7} + 69206 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(464))\) 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	29
464.8.a.a	$464$	$8$	464.a	1.a	$1$	$3$	$3$	$144.947$	3.3.1792765.1	None	✓				58.8.a.a	$1$	$1$	\(0\)	\(-13\)	\(195\)	\(-110\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-4+\beta _{1}+\beta _{2})q^{3}+(67-\beta _{1}+6\beta _{2})q^{5}+\cdots\)
464.8.a.b	$464$	$8$	464.a	1.a	$1$	$3$	$3$	$144.947$	3.3.732765.1	None	✓				58.8.a.b	$1$	$1$	\(0\)	\(25\)	\(-305\)	\(1138\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(8-\beta _{2})q^{3}+(-104+3\beta _{1}-4\beta _{2})q^{5}+\cdots\)
464.8.a.c	$464$	$8$	464.a	1.a	$1$	$4$	$4$	$144.947$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				58.8.a.c	$1$	$0$	\(0\)	\(68\)	\(-180\)	\(576\)		$-$	$-$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(17-\beta _{2})q^{3}+(-45-3\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
464.8.a.d	$464$	$8$	464.a	1.a	$1$	$5$	$5$	$144.947$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				58.8.a.d	$1$	$0$	\(0\)	\(-56\)	\(570\)	\(-920\)		$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-11-\beta _{1})q^{3}+(114-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
464.8.a.e	$464$	$8$	464.a	1.a	$1$	$7$	$7$	$144.947$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				116.8.a.a	$1$	$1$	\(0\)	\(0\)	\(-320\)	\(12\)		$-$	$+$	$-$	$2^{10}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-46-\beta _{4})q^{5}+(1-3\beta _{1}+\cdots)q^{7}+\cdots\)
464.8.a.f	$464$	$8$	464.a	1.a	$1$	$7$	$7$	$144.947$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				29.8.a.a	$1$	$0$	\(0\)	\(82\)	\(-320\)	\(1704\)		$-$	$-$	$+$	$2^{10}\cdot 7$	$\mathrm{SU}(2)$	\(q+(12-\beta _{2})q^{3}+(-45+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
464.8.a.g	$464$	$8$	464.a	1.a	$1$	$10$	$10$	$144.947$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		29.8.a.b	$1$	$1$	\(0\)	\(-80\)	\(180\)	\(-1040\)		$-$	$+$	$-$	$2^{26}$	$\mathrm{SU}(2)$	\(q+(-8-\beta _{2})q^{3}+(18+\beta _{2}+\beta _{5})q^{5}+\cdots\)
464.8.a.h	$464$	$8$	464.a	1.a	$1$	$10$	$10$	$144.947$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		116.8.a.b	$1$	$0$	\(0\)	\(0\)	\(180\)	\(-1360\)		$-$	$-$	$+$	$2^{19}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(18-\beta _{1}-\beta _{2})q^{5}+(-136+\cdots)q^{7}+\cdots\)
464.8.a.i	$464$	$8$	464.a	1.a	$1$	$11$	$11$	$144.947$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				232.8.a.a	$1$	$1$	\(0\)	\(42\)	\(-500\)	\(-784\)		$+$	$-$	$-$	$2^{25}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(4-\beta _{1})q^{3}+(-45-\beta _{1}-\beta _{5})q^{5}+\cdots\)
464.8.a.j	$464$	$8$	464.a	1.a	$1$	$12$	$12$	$144.947$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		232.8.a.b	$1$	$1$	\(0\)	\(-82\)	\(250\)	\(-2280\)		$+$	$-$	$-$	$2^{27}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-7+\beta _{1})q^{3}+(21-\beta _{1}-\beta _{2})q^{5}+\cdots\)
464.8.a.k	$464$	$8$	464.a	1.a	$1$	$13$	$13$	$144.947$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				232.8.a.d	$1$	$0$	\(0\)	\(-39\)	\(375\)	\(-98\)		$+$	$+$	$+$	$2^{37}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{3}+(29-\beta _{3})q^{5}+(-8+\cdots)q^{7}+\cdots\)
464.8.a.l	$464$	$8$	464.a	1.a	$1$	$13$	$13$	$144.947$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				232.8.a.c	$1$	$0$	\(0\)	\(-1\)	\(-125\)	\(1150\)		$+$	$+$	$+$	$2^{37}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-10-\beta _{1}-\beta _{2})q^{5}+(88+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(464))\) into lower level spaces

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