Space of modular forms of level 465, weight 4, and trivial character

• Label: 465.4.a
• Level: $465$
• Weight: $4$
• Character orbit: 465.a
• Rep. character: $\chi_{465}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $12$
• Sturm bound: $256$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	465.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(256\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(465))\).

	Total	New	Old
Modular forms	196	60	136
Cusp forms	188	60	128
Eisenstein series	8	0	8

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

\(3\)	\(5\)	\(31\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(8\)
\(+\)	\(+\)	\(-\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(-\)	$+$	\(9\)
\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(-\)	\(+\)	\(-\)	$+$	\(8\)
\(-\)	\(-\)	\(+\)	$+$	\(9\)
\(-\)	\(-\)	\(-\)	$-$	\(6\)
Plus space			\(+\)	\(34\)
Minus space			\(-\)	\(26\)

Trace form

\( 60 q - 8 q^{2} + 280 q^{4} - 56 q^{7} + 72 q^{8} + 540 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(465))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	31
465.4.a.a	$465$	$4$	465.a	1.a	$1$	$1$	$1$	$27.436$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(3\)	\(5\)	\(22\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+3q^{3}+8q^{4}+5q^{5}-12q^{6}+\cdots\)
465.4.a.b	$465$	$4$	465.a	1.a	$1$	$1$	$1$	$27.436$	\(\Q\)	None	✓	$1$	$2$	\(-3\)	\(-3\)	\(-5\)	\(-24\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}-3q^{3}+q^{4}-5q^{5}+9q^{6}+\cdots\)
465.4.a.c	$465$	$4$	465.a	1.a	$1$	$1$	$1$	$27.436$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(3\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
465.4.a.d	$465$	$4$	465.a	1.a	$1$	$2$	$2$	$27.436$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(2\)	\(6\)	\(-10\)	\(-7\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots\)
465.4.a.e	$465$	$4$	465.a	1.a	$1$	$4$	$4$	$27.436$	4.4.2862868.2	None	✓	$1$	$1$	\(-2\)	\(12\)	\(20\)	\(-64\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(3+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
465.4.a.f	$465$	$4$	465.a	1.a	$1$	$6$	$6$	$27.436$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(-18\)	\(30\)	\(-23\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
465.4.a.g	$465$	$4$	465.a	1.a	$1$	$6$	$6$	$27.436$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(18\)	\(-30\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(10-\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)
465.4.a.h	$465$	$4$	465.a	1.a	$1$	$7$	$7$	$27.436$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(21\)	\(-35\)	\(-49\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
465.4.a.i	$465$	$4$	465.a	1.a	$1$	$7$	$7$	$27.436$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-21\)	\(-35\)	\(-61\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
465.4.a.j	$465$	$4$	465.a	1.a	$1$	$7$	$7$	$27.436$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(-21\)	\(-35\)	\(61\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-3q^{3}+(6-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
465.4.a.k	$465$	$4$	465.a	1.a	$1$	$9$	$9$	$27.436$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(-27\)	\(45\)	\(19\)		$+$	$-$	$-$	$+$	$2^{9}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}+5q^{5}+\cdots\)
465.4.a.l	$465$	$4$	465.a	1.a	$1$	$9$	$9$	$27.436$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(27\)	\(45\)	\(63\)		$-$	$-$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(465))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(465)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 2}\)