Space of modular forms of level 460, weight 2, and trivial character

• Label: 460.2.a
• Level: $460$
• Weight: $2$
• Character orbit: 460.a
• Rep. character: $\chi_{460}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $5$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(460))\).

	Total	New	Old
Modular forms	78	6	72
Cusp forms	67	6	61
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.

\(2\)	\(5\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(8\)	\(0\)	\(8\)		\(7\)	\(0\)	\(7\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(11\)	\(0\)	\(11\)		\(9\)	\(0\)	\(9\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(12\)	\(0\)	\(12\)		\(10\)	\(0\)	\(10\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(9\)	\(0\)	\(9\)		\(7\)	\(0\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(10\)	\(2\)	\(8\)		\(9\)	\(2\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(10\)	\(1\)	\(9\)		\(9\)	\(1\)	\(8\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(9\)	\(1\)	\(8\)		\(8\)	\(1\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(9\)	\(2\)	\(7\)		\(8\)	\(2\)	\(6\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(36\)	\(2\)	\(34\)		\(31\)	\(2\)	\(29\)		\(5\)	\(0\)	\(5\)
Minus space			\(-\)		\(42\)	\(4\)	\(38\)		\(36\)	\(4\)	\(32\)		\(6\)	\(0\)	\(6\)

Trace form

6 * q + 4 * q^3 - 4 * q^7 + 2 * q^9 - 4 * q^15 + 12 * q^17 + 8 * q^19 - 4 * q^21 + 6 * q^25 + 16 * q^27 + 2 * q^29 - 2 * q^31 + 2 * q^35 - 20 * q^37 - 4 * q^39 - 2 * q^41 - 12 * q^47 - 8 * q^49 + 4 * q^51 - 4 * q^53 + 2 * q^59 - 20 * q^61 + 20 * q^63 - 4 * q^65 - 12 * q^67 + 42 * q^71 - 4 * q^73 + 4 * q^75 + 28 * q^77 - 12 * q^79 + 6 * q^81 - 4 * q^83 - 10 * q^85 + 4 * q^87 - 12 * q^89 - 20 * q^91 - 20 * q^93 + 8 * q^95 - 8 * q^97 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(460))\) 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	5	23
460.2.a.a	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	\(\Q\)	None	✓	✓	✓	✓	460.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
460.2.a.b	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	\(\Q\)	None	✓	✓			460.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots\)
460.2.a.c	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	\(\Q\)	None	✓	✓	✓	✓	460.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
460.2.a.d	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	\(\Q\)	None	✓	✓			460.2.a.d	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+2q^{7}+6q^{9}-3q^{13}+\cdots\)
460.2.a.e	$460$	$2$	460.a	1.a	$1$	$2$	$2$	$3.673$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	460.2.a.e	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(460))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(460)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 2}\)