Space of modular forms of level 4527, weight 2, and trivial character

• Label: 4527.2.a
• Level: $4527$
• Weight: $2$
• Character orbit: 4527.a
• Rep. character: $\chi_{4527}(1,\cdot)$
• Character field: $\Q$
• Dimension: $209$
• Newform subspaces: $18$
• Sturm bound: $1008$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4527 = 3^{2} \cdot 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4527.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1008\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4527))\).

	Total	New	Old
Modular forms	508	209	299
Cusp forms	501	209	292
Eisenstein series	7	0	7

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

\(3\)	\(503\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(42\)
\(+\)	\(-\)	$-$	\(42\)
\(-\)	\(+\)	$-$	\(73\)
\(-\)	\(-\)	$+$	\(52\)
Plus space		\(+\)	\(94\)
Minus space		\(-\)	\(115\)

Trace form

\( 209 q + 2 q^{2} + 210 q^{4} + 2 q^{5} - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4527))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	503
4527.2.a.a	$4527$	$2$	4527.a	1.a	$1$	$1$	$1$	$36.148$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{5}+3q^{8}+4q^{10}+\cdots\)
4527.2.a.b	$4527$	$2$	4527.a	1.a	$1$	$1$	$1$	$36.148$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-3q^{7}+3q^{8}+q^{10}+\cdots\)
4527.2.a.c	$4527$	$2$	4527.a	1.a	$1$	$1$	$1$	$36.148$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}-3q^{7}+3q^{8}-2q^{10}+\cdots\)
4527.2.a.d	$4527$	$2$	4527.a	1.a	$1$	$1$	$1$	$36.148$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+3q^{7}+3q^{8}-2q^{10}+\cdots\)
4527.2.a.e	$4527$	$2$	4527.a	1.a	$1$	$1$	$1$	$36.148$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-3q^{7}-3q^{8}+q^{10}+\cdots\)
4527.2.a.f	$4527$	$2$	4527.a	1.a	$1$	$1$	$1$	$36.148$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+3q^{7}-3q^{8}+q^{10}+\cdots\)
4527.2.a.g	$4527$	$2$	4527.a	1.a	$1$	$1$	$1$	$36.148$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(4\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{5}-3q^{7}-3q^{8}+4q^{10}+\cdots\)
4527.2.a.h	$4527$	$2$	4527.a	1.a	$1$	$2$	$2$	$36.148$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-\beta q^{5}+2q^{7}+3q^{8}+\beta q^{10}+\cdots\)
4527.2.a.i	$4527$	$2$	4527.a	1.a	$1$	$2$	$2$	$36.148$	\(\Q(\sqrt{29}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-\beta q^{5}-2q^{7}-3q^{8}-\beta q^{10}+\cdots\)
4527.2.a.j	$4527$	$2$	4527.a	1.a	$1$	$3$	$3$	$36.148$	3.3.257.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
4527.2.a.k	$4527$	$2$	4527.a	1.a	$1$	$10$	$10$	$36.148$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(4\)	\(0\)	\(1\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{9}q^{2}+\beta _{5}q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
4527.2.a.l	$4527$	$2$	4527.a	1.a	$1$	$13$	$13$	$36.148$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(12\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)
4527.2.a.m	$4527$	$2$	4527.a	1.a	$1$	$14$	$14$	$36.148$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(5\)	\(-11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4527.2.a.n	$4527$	$2$	4527.a	1.a	$1$	$24$	$24$	$36.148$		None	✓	$1$	$1$	\(-5\)	\(0\)	\(-8\)	\(1\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4527.2.a.o	$4527$	$2$	4527.a	1.a	$1$	$26$	$26$	$36.148$		None	✓	$1$	$0$	\(-4\)	\(0\)	\(-9\)	\(11\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
4527.2.a.p	$4527$	$2$	4527.a	1.a	$1$	$26$	$26$	$36.148$		None	✓	$1$	$0$	\(3\)	\(0\)	\(-2\)	\(9\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
4527.2.a.q	$4527$	$2$	4527.a	1.a	$1$	$41$	$41$	$36.148$		None	✓	$1$	$1$	\(-9\)	\(0\)	\(-11\)	\(1\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4527.2.a.r	$4527$	$2$	4527.a	1.a	$1$	$41$	$41$	$36.148$		None	✓	$1$	$0$	\(9\)	\(0\)	\(11\)	\(1\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4527))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4527)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1509))\)\(^{\oplus 2}\)