Space of modular forms of level 464, weight 2, and trivial character

• Label: 464.2.a
• Level: $464$
• Weight: $2$
• Character orbit: 464.a
• Rep. character: $\chi_{464}(1,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $10$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(464))\).

	Total	New	Old
Modular forms	66	14	52
Cusp forms	55	14	41
Eisenstein series	11	0	11

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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(13\)	\(2\)	\(11\)		\(11\)	\(2\)	\(9\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(19\)	\(5\)	\(14\)		\(16\)	\(5\)	\(11\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)		\(20\)	\(5\)	\(15\)		\(17\)	\(5\)	\(12\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)		\(14\)	\(2\)	\(12\)		\(11\)	\(2\)	\(9\)		\(3\)	\(0\)	\(3\)
Plus space		\(+\)		\(27\)	\(4\)	\(23\)		\(22\)	\(4\)	\(18\)		\(5\)	\(0\)	\(5\)
Minus space		\(-\)		\(39\)	\(10\)	\(29\)		\(33\)	\(10\)	\(23\)		\(6\)	\(0\)	\(6\)

Trace form

14 * q + 2 * q^3 + 4 * q^7 + 10 * q^9 + 6 * q^11 + 8 * q^15 - 4 * q^17 + 2 * q^19 + 12 * q^23 + 14 * q^25 + 20 * q^27 + 2 * q^31 - 4 * q^39 - 4 * q^41 + 6 * q^43 + 2 * q^47 + 14 * q^49 - 28 * q^51 - 12 * q^55 - 8 * q^57 - 4 * q^59 + 16 * q^61 - 4 * q^63 - 24 * q^65 - 8 * q^67 - 16 * q^71 - 4 * q^73 + 10 * q^75 - 16 * q^77 + 22 * q^79 - 10 * q^81 - 28 * q^83 - 6 * q^87 - 12 * q^89 + 16 * q^91 - 32 * q^93 - 48 * q^95 - 4 * q^97 - 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(464))\) 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
464.2.a.a	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	\(\Q\)	None	✓				116.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
464.2.a.b	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	\(\Q\)	None	✓				232.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}-2q^{9}-3q^{11}+\cdots\)
464.2.a.c	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	\(\Q\)	None	✓				116.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+4q^{7}-2q^{9}-3q^{11}+\cdots\)
464.2.a.d	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	\(\Q\)	None	✓				232.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{7}-2q^{9}+3q^{11}+\cdots\)
464.2.a.e	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	\(\Q\)	None	✓				58.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\)
464.2.a.f	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	\(\Q\)	None	✓				58.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots\)
464.2.a.g	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	\(\Q\)	None	✓				116.2.a.a	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+3q^{5}-4q^{7}+6q^{9}+q^{11}+\cdots\)
464.2.a.h	$464$	$2$	464.a	1.a	$1$	$2$	$2$	$3.705$	\(\Q(\sqrt{2}) \)	None	✓		✓	✓	29.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{7}-2\beta q^{9}+\cdots\)
464.2.a.i	$464$	$2$	464.a	1.a	$1$	$2$	$2$	$3.705$	\(\Q(\sqrt{2}) \)	None	✓				232.2.a.c	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+4q^{7}+\cdots\)
464.2.a.j	$464$	$2$	464.a	1.a	$1$	$3$	$3$	$3.705$	3.3.568.1	None	✓		✓		232.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(464))\) into lower level spaces

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