Space of modular forms of level 2527, weight 2, and trivial character

• Label: 2527.2.a
• Level: $2527$
• Weight: $2$
• Character orbit: 2527.a
• Rep. character: $\chi_{2527}(1,\cdot)$
• Character field: $\Q$
• Dimension: $171$
• Newform subspaces: $22$
• Sturm bound: $506$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2527 = 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2527.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(506\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2527))\).

	Total	New	Old
Modular forms	272	171	101
Cusp forms	233	171	62
Eisenstein series	39	0	39

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

\(7\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(40\)
\(+\)	\(-\)	$-$	\(45\)
\(-\)	\(+\)	$-$	\(50\)
\(-\)	\(-\)	$+$	\(36\)
Plus space		\(+\)	\(76\)
Minus space		\(-\)	\(95\)

Trace form

\( 171 q + q^{2} + 169 q^{4} + 6 q^{5} + q^{7} + 9 q^{8} + 171 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2527))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	19
2527.2.a.a	$2527$	$2$	2527.a	1.a	$1$	$2$	$2$	$20.178$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
2527.2.a.b	$2527$	$2$	2527.a	1.a	$1$	$2$	$2$	$20.178$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
2527.2.a.c	$2527$	$2$	2527.a	1.a	$1$	$2$	$2$	$20.178$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
2527.2.a.d	$2527$	$2$	2527.a	1.a	$1$	$2$	$2$	$20.178$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(1\)	\(3\)	\(-6\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2-\beta )q^{3}+(1+\beta )q^{4}-3q^{5}+\cdots\)
2527.2.a.e	$2527$	$2$	2527.a	1.a	$1$	$2$	$2$	$20.178$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(3\)	\(3\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots\)
2527.2.a.f	$2527$	$2$	2527.a	1.a	$1$	$3$	$3$	$20.178$	3.3.229.1	None	✓	$1$	$0$	\(-2\)	\(-3\)	\(-2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots\)
2527.2.a.g	$2527$	$2$	2527.a	1.a	$1$	$3$	$3$	$20.178$	3.3.321.1	None	✓	$1$	$1$	\(-2\)	\(-1\)	\(-3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2527.2.a.h	$2527$	$2$	2527.a	1.a	$1$	$3$	$3$	$20.178$	3.3.321.1	None	✓	$1$	$0$	\(2\)	\(1\)	\(-3\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2527.2.a.i	$2527$	$2$	2527.a	1.a	$1$	$4$	$4$	$20.178$	4.4.240944.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(3+\beta _{2})q^{4}-q^{5}+\cdots\)
2527.2.a.j	$2527$	$2$	2527.a	1.a	$1$	$5$	$5$	$20.178$	5.5.210557.1	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(1\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2527.2.a.k	$2527$	$2$	2527.a	1.a	$1$	$5$	$5$	$20.178$	5.5.210557.1	None	✓	$1$	$0$	\(1\)	\(3\)	\(1\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2527.2.a.l	$2527$	$2$	2527.a	1.a	$1$	$6$	$6$	$20.178$	6.6.1416125.1	None	✓	$1$	$1$	\(-1\)	\(2\)	\(-5\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{3})q^{4}+\cdots\)
2527.2.a.m	$2527$	$2$	2527.a	1.a	$1$	$6$	$6$	$20.178$	6.6.171932480.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(4\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
2527.2.a.n	$2527$	$2$	2527.a	1.a	$1$	$6$	$6$	$20.178$	6.6.1416125.1	None	✓	$1$	$1$	\(1\)	\(-2\)	\(-5\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{3})q^{4}+\cdots\)
2527.2.a.o	$2527$	$2$	2527.a	1.a	$1$	$10$	$10$	$20.178$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(11\)	\(-10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{9})q^{3}+(\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
2527.2.a.p	$2527$	$2$	2527.a	1.a	$1$	$10$	$10$	$20.178$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(11\)	\(-10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{9})q^{3}+(\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2527.2.a.q	$2527$	$2$	2527.a	1.a	$1$	$15$	$15$	$20.178$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-9\)	\(-6\)	\(0\)	\(15\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{12}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
2527.2.a.r	$2527$	$2$	2527.a	1.a	$1$	$15$	$15$	$20.178$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(-6\)	\(0\)	\(-15\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)
2527.2.a.s	$2527$	$2$	2527.a	1.a	$1$	$15$	$15$	$20.178$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(6\)	\(0\)	\(-15\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)
2527.2.a.t	$2527$	$2$	2527.a	1.a	$1$	$15$	$15$	$20.178$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(9\)	\(6\)	\(0\)	\(15\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{12}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2527.2.a.u	$2527$	$2$	2527.a	1.a	$1$	$16$	$16$	$20.178$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-16\)	\(-16\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{13}q^{2}+\beta _{15}q^{3}+(\beta _{6}+\beta _{8})q^{4}+\cdots\)
2527.2.a.v	$2527$	$2$	2527.a	1.a	$1$	$24$	$24$	$20.178$		None	✓	$2$	$0$	\(0\)	\(0\)	\(16\)	\(24\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2527))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2527)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 2}\)