Space of modular forms of level 2523, weight 2, and trivial character

• Label: 2523.2.a
• Level: $2523$
• Weight: $2$
• Character orbit: 2523.a
• Rep. character: $\chi_{2523}(1,\cdot)$
• Character field: $\Q$
• Dimension: $135$
• Newform subspaces: $22$
• Sturm bound: $580$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2523.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(580\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2523))\).

	Total	New	Old
Modular forms	320	135	185
Cusp forms	261	135	126
Eisenstein series	59	0	59

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

\(3\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(32\)
\(+\)	\(-\)	\(-\)	\(35\)
\(-\)	\(+\)	\(-\)	\(42\)
\(-\)	\(-\)	\(+\)	\(26\)
Plus space		\(+\)	\(58\)
Minus space		\(-\)	\(77\)

Trace form

135 * q - 3 * q^2 + q^3 + 135 * q^4 - 2 * q^5 + q^6 - 3 * q^8 + 135 * q^9 + 10 * q^10 + 4 * q^11 + 7 * q^12 - 2 * q^13 + 12 * q^14 - 2 * q^15 + 147 * q^16 - 10 * q^17 - 3 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 - 4 * q^23 - 3 * q^24 + 121 * q^25 + 2 * q^26 + q^27 - 16 * q^28 - 2 * q^30 + q^32 - 12 * q^33 - 10 * q^34 + 4 * q^35 + 135 * q^36 - 14 * q^37 - 20 * q^38 + 6 * q^39 + 22 * q^40 - 2 * q^41 - 4 * q^42 - 4 * q^43 + 8 * q^44 - 2 * q^45 - 12 * q^46 + 16 * q^47 - q^48 + 139 * q^49 - 45 * q^50 - 2 * q^51 - 14 * q^52 - 26 * q^53 + q^54 + 16 * q^55 - 24 * q^56 + 8 * q^57 + 16 * q^59 - 10 * q^60 + 2 * q^61 + 16 * q^62 + 135 * q^64 - 20 * q^66 - 26 * q^68 + 8 * q^69 + 20 * q^70 + 20 * q^71 - 3 * q^72 - 10 * q^73 + 14 * q^74 + 15 * q^75 - 12 * q^76 + 16 * q^77 - 26 * q^78 + 32 * q^79 + 6 * q^80 + 135 * q^81 + 10 * q^82 + 16 * q^83 + 16 * q^84 + 36 * q^85 - 52 * q^86 - 4 * q^88 - 2 * q^89 + 10 * q^90 - 4 * q^91 - 32 * q^92 + 12 * q^93 - 8 * q^94 + 32 * q^95 + 5 * q^96 - 10 * q^97 + 9 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2523))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	29
2523.2.a.a	$2523$	$2$	2523.a	1.a	$1$	$2$	$2$	$20.146$	\(\Q(\sqrt{5}) \)	None	✓	✓			2523.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(-3\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2523.2.a.b	$2523$	$2$	2523.a	1.a	$1$	$2$	$2$	$20.146$	\(\Q(\sqrt{5}) \)	None	✓	✓			2523.2.a.b	$1$	$1$	\(-1\)	\(-2\)	\(-1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2523.2.a.c	$2523$	$2$	2523.a	1.a	$1$	$2$	$2$	$20.146$	\(\Q(\sqrt{5}) \)	None	✓				87.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
2523.2.a.d	$2523$	$2$	2523.a	1.a	$1$	$2$	$2$	$20.146$	\(\Q(\sqrt{5}) \)	None	✓				87.2.c.a	$1$	$1$	\(-1\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-2\beta q^{5}+\cdots\)
2523.2.a.e	$2523$	$2$	2523.a	1.a	$1$	$2$	$2$	$20.146$	\(\Q(\sqrt{5}) \)	None	✓				87.2.c.a	$1$	$0$	\(1\)	\(-2\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-2\beta q^{5}+\cdots\)
2523.2.a.f	$2523$	$2$	2523.a	1.a	$1$	$2$	$2$	$20.146$	\(\Q(\sqrt{5}) \)	None	✓	✓			2523.2.a.a	$1$	$1$	\(1\)	\(2\)	\(-3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2523.2.a.g	$2523$	$2$	2523.a	1.a	$1$	$2$	$2$	$20.146$	\(\Q(\sqrt{5}) \)	None	✓	✓			2523.2.a.b	$1$	$1$	\(1\)	\(2\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2523.2.a.h	$2523$	$2$	2523.a	1.a	$1$	$3$	$3$	$20.146$	3.3.229.1	None	✓				87.2.a.b	$1$	$0$	\(-2\)	\(3\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots\)
2523.2.a.i	$2523$	$2$	2523.a	1.a	$1$	$3$	$3$	$20.146$	3.3.733.1	None	✓	✓			2523.2.a.i	$1$	$0$	\(-1\)	\(-3\)	\(3\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
2523.2.a.j	$2523$	$2$	2523.a	1.a	$1$	$3$	$3$	$20.146$	3.3.733.1	None	✓	✓			2523.2.a.i	$1$	$0$	\(1\)	\(3\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(3+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
2523.2.a.k	$2523$	$2$	2523.a	1.a	$1$	$6$	$6$	$20.146$	6.6.8902000.1	None	✓	✓			2523.2.a.k	$1$	$0$	\(-1\)	\(-6\)	\(5\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2523.2.a.l	$2523$	$2$	2523.a	1.a	$1$	$6$	$6$	$20.146$	6.6.8902000.1	None	✓	✓			2523.2.a.k	$1$	$0$	\(1\)	\(6\)	\(5\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2523.2.a.m	$2523$	$2$	2523.a	1.a	$1$	$8$	$8$	$20.146$	8.8.5878828125.1	None	✓	✓			2523.2.a.m	$1$	$1$	\(-1\)	\(8\)	\(-9\)	\(-12\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2523.2.a.n	$2523$	$2$	2523.a	1.a	$1$	$8$	$8$	$20.146$	8.8.5878828125.1	None	✓	✓			2523.2.a.m	$1$	$1$	\(1\)	\(-8\)	\(-9\)	\(-12\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2523.2.a.o	$2523$	$2$	2523.a	1.a	$1$	$9$	$9$	$20.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.a	$1$	$1$	\(-5\)	\(-9\)	\(-4\)	\(5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
2523.2.a.p	$2523$	$2$	2523.a	1.a	$1$	$9$	$9$	$20.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.b	$1$	$1$	\(-1\)	\(-9\)	\(0\)	\(5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
2523.2.a.q	$2523$	$2$	2523.a	1.a	$1$	$9$	$9$	$20.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.b	$1$	$0$	\(1\)	\(9\)	\(0\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
2523.2.a.r	$2523$	$2$	2523.a	1.a	$1$	$9$	$9$	$20.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.a	$1$	$0$	\(5\)	\(9\)	\(-4\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2523.2.a.s	$2523$	$2$	2523.a	1.a	$1$	$12$	$12$	$20.146$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		87.2.i.a	$1$	$1$	\(-6\)	\(12\)	\(2\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2523.2.a.t	$2523$	$2$	2523.a	1.a	$1$	$12$	$12$	$20.146$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		2523.2.a.t	$1$	$0$	\(-1\)	\(12\)	\(7\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{3}-\beta _{6}+\beta _{9}+\cdots)q^{4}+\cdots\)
2523.2.a.u	$2523$	$2$	2523.a	1.a	$1$	$12$	$12$	$20.146$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2523.2.a.t	$1$	$0$	\(1\)	\(-12\)	\(7\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}-\beta _{6}+\beta _{9}+\cdots)q^{4}+\cdots\)
2523.2.a.v	$2523$	$2$	2523.a	1.a	$1$	$12$	$12$	$20.146$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				87.2.i.a	$1$	$0$	\(6\)	\(-12\)	\(2\)	\(-10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2523))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2523)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(841))\)\(^{\oplus 2}\)