Space of modular forms of level 2023, weight 4, and trivial character

• Label: 2023.4.a
• Level: $2023$
• Weight: $4$
• Character orbit: 2023.a
• Rep. character: $\chi_{2023}(1,\cdot)$
• Character field: $\Q$
• Dimension: $407$
• Newform subspaces: $22$
• Sturm bound: $816$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(816\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2023))\).

	Total	New	Old
Modular forms	630	407	223
Cusp forms	594	407	187
Eisenstein series	36	0	36

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

\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(162\)	\(104\)	\(58\)		\(153\)	\(104\)	\(49\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)		\(153\)	\(100\)	\(53\)		\(144\)	\(100\)	\(44\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)		\(153\)	\(95\)	\(58\)		\(144\)	\(95\)	\(49\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)		\(162\)	\(108\)	\(54\)		\(153\)	\(108\)	\(45\)		\(9\)	\(0\)	\(9\)
Plus space		\(+\)		\(324\)	\(212\)	\(112\)		\(306\)	\(212\)	\(94\)		\(18\)	\(0\)	\(18\)
Minus space		\(-\)		\(306\)	\(195\)	\(111\)		\(288\)	\(195\)	\(93\)		\(18\)	\(0\)	\(18\)

Trace form

407 * q - q^2 - 6 * q^3 + 1649 * q^4 - 62 * q^6 - 7 * q^7 + 15 * q^8 + 3759 * q^9 - 128 * q^10 - 60 * q^11 - 34 * q^12 - 28 * q^13 + 7 * q^14 + 96 * q^15 + 6561 * q^16 - 233 * q^18 + 110 * q^19 - 320 * q^20 - 14 * q^21 + 224 * q^22 - 64 * q^23 - 1158 * q^24 + 9717 * q^25 + 44 * q^26 - 300 * q^27 + 49 * q^28 - 694 * q^29 + 804 * q^30 - 44 * q^31 + 919 * q^32 - 168 * q^33 + 168 * q^35 + 17437 * q^36 + 234 * q^37 + 982 * q^38 + 640 * q^39 + 724 * q^40 - 542 * q^41 + 14 * q^42 - 572 * q^43 + 56 * q^44 + 112 * q^45 - 168 * q^46 + 1284 * q^47 + 3162 * q^48 + 19943 * q^49 + 1409 * q^50 + 232 * q^52 - 422 * q^53 + 1728 * q^54 + 352 * q^55 - 105 * q^56 - 1180 * q^57 - 1630 * q^58 + 582 * q^59 + 2884 * q^60 - 568 * q^61 + 4076 * q^62 + 273 * q^63 + 25633 * q^64 - 384 * q^65 + 3392 * q^66 - 816 * q^67 - 1000 * q^69 - 616 * q^70 - 232 * q^71 + 455 * q^72 + 838 * q^73 - 42 * q^74 - 922 * q^75 - 2934 * q^76 + 896 * q^77 + 940 * q^78 - 3160 * q^79 - 720 * q^80 + 33627 * q^81 + 2842 * q^82 - 618 * q^83 + 98 * q^84 + 2176 * q^86 - 36 * q^87 - 2860 * q^88 - 4274 * q^89 - 700 * q^90 - 532 * q^91 + 5512 * q^92 + 2840 * q^93 - 1888 * q^94 - 1176 * q^95 - 1070 * q^96 + 194 * q^97 - 49 * q^98 - 6396 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2023))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	17
2023.4.a.a	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	\(\Q\)	None	✓				7.4.a.a	$1$	$1$	\(-1\)	\(2\)	\(-16\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots\)
2023.4.a.b	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	\(\Q\)	None	✓				119.4.a.a	$1$	$1$	\(-1\)	\(6\)	\(20\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+6q^{3}-7q^{4}+20q^{5}-6q^{6}+\cdots\)
2023.4.a.c	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	\(\Q\)	None	✓	✓			2023.4.a.c	$1$	$0$	\(3\)	\(-1\)	\(6\)	\(-7\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-q^{3}+q^{4}+6q^{5}-3q^{6}-7q^{7}+\cdots\)
2023.4.a.d	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	\(\Q\)	None	✓	✓			2023.4.a.c	$1$	$0$	\(3\)	\(1\)	\(-6\)	\(7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+q^{3}+q^{4}-6q^{5}+3q^{6}+7q^{7}+\cdots\)
2023.4.a.e	$2023$	$4$	2023.a	1.a	$1$	$3$	$3$	$119.361$	3.3.2429.1	None	✓				119.4.a.b	$1$	$1$	\(-1\)	\(-5\)	\(19\)	\(21\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
2023.4.a.f	$2023$	$4$	2023.a	1.a	$1$	$4$	$4$	$119.361$	4.4.68557.1	None	✓				119.4.a.c	$1$	$0$	\(-2\)	\(7\)	\(9\)	\(-28\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
2023.4.a.g	$2023$	$4$	2023.a	1.a	$1$	$7$	$7$	$119.361$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				119.4.a.d	$1$	$1$	\(4\)	\(-5\)	\(-35\)	\(49\)		$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots\)
2023.4.a.h	$2023$	$4$	2023.a	1.a	$1$	$9$	$9$	$119.361$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				119.4.a.e	$1$	$0$	\(2\)	\(-11\)	\(3\)	\(-63\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
2023.4.a.i	$2023$	$4$	2023.a	1.a	$1$	$11$	$11$	$119.361$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			2023.4.a.i	$1$	$1$	\(-7\)	\(-2\)	\(2\)	\(-77\)		$+$	$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.4.a.j	$2023$	$4$	2023.a	1.a	$1$	$11$	$11$	$119.361$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			2023.4.a.i	$1$	$1$	\(-7\)	\(2\)	\(-2\)	\(77\)		$-$	$+$	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.4.a.k	$2023$	$4$	2023.a	1.a	$1$	$12$	$12$	$119.361$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2023.4.a.k	$1$	$0$	\(3\)	\(-3\)	\(12\)	\(84\)		$-$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.4.a.l	$2023$	$4$	2023.a	1.a	$1$	$12$	$12$	$119.361$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2023.4.a.k	$1$	$0$	\(3\)	\(3\)	\(-12\)	\(-84\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.4.a.m	$2023$	$4$	2023.a	1.a	$1$	$13$	$13$	$119.361$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				119.4.b.a	$1$	$1$	\(0\)	\(-14\)	\(-20\)	\(91\)		$-$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2023.4.a.n	$2023$	$4$	2023.a	1.a	$1$	$13$	$13$	$119.361$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				119.4.b.a	$1$	$0$	\(0\)	\(14\)	\(20\)	\(-91\)		$+$	$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2023.4.a.o	$2023$	$4$	2023.a	1.a	$1$	$26$	$26$	$119.361$		None	✓				119.4.g.a	$1$	$1$	\(-8\)	\(-12\)	\(-40\)	\(182\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2023.4.a.p	$2023$	$4$	2023.a	1.a	$1$	$26$	$26$	$119.361$		None	✓				119.4.g.a	$1$	$0$	\(-8\)	\(12\)	\(40\)	\(-182\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2023.4.a.q	$2023$	$4$	2023.a	1.a	$1$	$33$	$33$	$119.361$		None	✓	✓			2023.4.a.q	$1$	$1$	\(-12\)	\(0\)	\(0\)	\(-231\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2023.4.a.r	$2023$	$4$	2023.a	1.a	$1$	$33$	$33$	$119.361$		None	✓	✓	✓		2023.4.a.q	$1$	$1$	\(-12\)	\(0\)	\(0\)	\(231\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2023.4.a.s	$2023$	$4$	2023.a	1.a	$1$	$39$	$39$	$119.361$		None	✓	✓			2023.4.a.s	$1$	$0$	\(12\)	\(0\)	\(0\)	\(273\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2023.4.a.t	$2023$	$4$	2023.a	1.a	$1$	$39$	$39$	$119.361$		None	✓	✓	✓		2023.4.a.s	$1$	$0$	\(12\)	\(0\)	\(0\)	\(-273\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2023.4.a.u	$2023$	$4$	2023.a	1.a	$1$	$56$	$56$	$119.361$		None	✓		✓		119.4.k.a	$1$	$1$	\(8\)	\(-24\)	\(-80\)	\(-392\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2023.4.a.v	$2023$	$4$	2023.a	1.a	$1$	$56$	$56$	$119.361$		None	✓		✓		119.4.k.a	$1$	$0$	\(8\)	\(24\)	\(80\)	\(392\)		$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2023))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2023)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)