Space of modular forms of level 920, weight 2, and trivial character

• Label: 920.2.a
• Level: $920$
• Weight: $2$
• Character orbit: 920.a
• Rep. character: $\chi_{920}(1,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $10$
• Sturm bound: $288$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(288\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(920))\).

	Total	New	Old
Modular forms	152	22	130
Cusp forms	137	22	115
Eisenstein series	15	0	15

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
\(+\)	\(+\)	\(+\)	\(+\)		\(15\)	\(2\)	\(13\)		\(14\)	\(2\)	\(12\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(22\)	\(3\)	\(19\)		\(20\)	\(3\)	\(17\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(21\)	\(3\)	\(18\)		\(19\)	\(3\)	\(16\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(18\)	\(2\)	\(16\)		\(16\)	\(2\)	\(14\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(23\)	\(5\)	\(18\)		\(21\)	\(5\)	\(16\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)		\(16\)	\(1\)	\(15\)		\(14\)	\(1\)	\(13\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)		\(17\)	\(1\)	\(16\)		\(15\)	\(1\)	\(14\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)		\(20\)	\(5\)	\(15\)		\(18\)	\(5\)	\(13\)		\(2\)	\(0\)	\(2\)
Plus space			\(+\)		\(66\)	\(6\)	\(60\)		\(59\)	\(6\)	\(53\)		\(7\)	\(0\)	\(7\)
Minus space			\(-\)		\(86\)	\(16\)	\(70\)		\(78\)	\(16\)	\(62\)		\(8\)	\(0\)	\(8\)

Trace form

22 * q + 8 * q^7 + 34 * q^9 - 4 * q^11 + 4 * q^13 + 4 * q^17 - 4 * q^19 + 8 * q^21 + 22 * q^25 - 8 * q^29 + 32 * q^31 + 24 * q^33 + 12 * q^35 + 8 * q^37 + 32 * q^39 + 12 * q^41 + 20 * q^43 + 22 * q^49 + 16 * q^51 + 24 * q^53 + 32 * q^57 - 12 * q^59 + 32 * q^61 - 12 * q^67 - 16 * q^71 + 36 * q^73 - 16 * q^77 - 16 * q^79 + 38 * q^81 - 28 * q^83 - 4 * q^85 - 48 * q^87 - 12 * q^89 + 24 * q^91 - 32 * q^93 - 8 * q^95 + 28 * q^97 - 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(920))\) 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
920.2.a.a	$920$	$2$	920.a	1.a	$1$	$1$	$1$	$7.346$	\(\Q\)	None	✓	✓			920.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}-2q^{7}+6q^{9}+q^{13}+\cdots\)
920.2.a.b	$920$	$2$	920.a	1.a	$1$	$1$	$1$	$7.346$	\(\Q\)	None	✓	✓	✓	✓	920.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}+2q^{11}-5q^{13}+\cdots\)
920.2.a.c	$920$	$2$	920.a	1.a	$1$	$1$	$1$	$7.346$	\(\Q\)	None	✓	✓			920.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots\)
920.2.a.d	$920$	$2$	920.a	1.a	$1$	$1$	$1$	$7.346$	\(\Q\)	None	✓	✓	✓	✓	920.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}-2q^{9}+q^{13}-q^{15}+\cdots\)
920.2.a.e	$920$	$2$	920.a	1.a	$1$	$2$	$2$	$7.346$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	920.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
920.2.a.f	$920$	$2$	920.a	1.a	$1$	$2$	$2$	$7.346$	\(\Q(\sqrt{17}) \)	None	✓	✓			920.2.a.f	$1$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+2\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
920.2.a.g	$920$	$2$	920.a	1.a	$1$	$3$	$3$	$7.346$	3.3.621.1	None	✓	✓	✓	✓	920.2.a.g	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
920.2.a.h	$920$	$2$	920.a	1.a	$1$	$3$	$3$	$7.346$	3.3.2597.1	None	✓	✓	✓		920.2.a.h	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
920.2.a.i	$920$	$2$	920.a	1.a	$1$	$3$	$3$	$7.346$	3.3.229.1	None	✓	✓	✓	✓	920.2.a.i	$1$	$0$	\(0\)	\(2\)	\(3\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+q^{5}+(2-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
920.2.a.j	$920$	$2$	920.a	1.a	$1$	$5$	$5$	$7.346$	5.5.13955077.1	None	✓	✓	✓	✓	920.2.a.j	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(920)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 2}\)