Space of modular forms of level 4563, weight 2, and trivial character

• Label: 4563.2.a
• Level: $4563$
• Weight: $2$
• Character orbit: 4563.a
• Rep. character: $\chi_{4563}(1,\cdot)$
• Character field: $\Q$
• Dimension: $207$
• Newform subspaces: $45$
• Sturm bound: $1092$
• Trace bound: $43$

Defining parameters

Level:	\( N \)	\(=\)	\( 4563 = 3^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4563.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 45 \)
Sturm bound:			\(1092\)
Trace bound:			\(43\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4563))\).

	Total	New	Old
Modular forms	588	207	381
Cusp forms	505	207	298
Eisenstein series	83	0	83

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

\(3\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(48\)
\(+\)	\(-\)	$-$	\(56\)
\(-\)	\(+\)	$-$	\(55\)
\(-\)	\(-\)	$+$	\(48\)
Plus space		\(+\)	\(96\)
Minus space		\(-\)	\(111\)

Trace form

\( 207 q + 206 q^{4} - 3 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4563))\) 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	13
4563.2.a.a	$4563$	$2$	4563.a	1.a	$1$	$1$	$1$	$36.436$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{5}-q^{7}-4q^{10}+\cdots\)
4563.2.a.b	$4563$	$2$	4563.a	1.a	$1$	$1$	$1$	$36.436$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{5}+q^{7}-4q^{10}+\cdots\)
4563.2.a.c	$4563$	$2$	4563.a	1.a	$1$	$1$	$1$	$36.436$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-q^{7}+4q^{16}-q^{19}-5q^{25}+\cdots\)
4563.2.a.d	$4563$	$2$	4563.a	1.a	$1$	$1$	$1$	$36.436$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+q^{7}+4q^{16}+q^{19}-5q^{25}+\cdots\)
4563.2.a.e	$4563$	$2$	4563.a	1.a	$1$	$1$	$1$	$36.436$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+q^{7}+4q^{16}+7q^{19}-5q^{25}+\cdots\)
4563.2.a.f	$4563$	$2$	4563.a	1.a	$1$	$1$	$1$	$36.436$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{5}-q^{7}-4q^{10}+\cdots\)
4563.2.a.g	$4563$	$2$	4563.a	1.a	$1$	$1$	$1$	$36.436$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{5}+q^{7}-4q^{10}+\cdots\)
4563.2.a.h	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
4563.2.a.i	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-5\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+(-3+\beta )q^{5}+q^{7}+\cdots\)
4563.2.a.j	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$3$	$N(\mathrm{U}(1))$	\(q-2q^{4}-\beta q^{7}+4q^{16}-\beta q^{19}-5q^{25}+\cdots\)
4563.2.a.k	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+3\beta q^{7}+4q^{16}-5\beta q^{19}+\cdots\)
4563.2.a.l	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-2\beta q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
4563.2.a.m	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-2\beta q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
4563.2.a.n	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+2\beta q^{5}-\beta q^{8}+6q^{10}+\cdots\)
4563.2.a.o	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+2\beta q^{5}-\beta q^{8}+6q^{10}+\cdots\)
4563.2.a.p	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+(1+\cdots)q^{7}+\cdots\)
4563.2.a.q	$4563$	$2$	4563.a	1.a	$1$	$2$	$2$	$36.436$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(5\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}+q^{7}+\cdots\)
4563.2.a.r	$4563$	$2$	4563.a	1.a	$1$	$3$	$3$	$36.436$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
4563.2.a.s	$4563$	$2$	4563.a	1.a	$1$	$3$	$3$	$36.436$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-1\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
4563.2.a.t	$4563$	$2$	4563.a	1.a	$1$	$3$	$3$	$36.436$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
4563.2.a.u	$4563$	$2$	4563.a	1.a	$1$	$3$	$3$	$36.436$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
4563.2.a.v	$4563$	$2$	4563.a	1.a	$1$	$4$	$4$	$36.436$	\(\Q(\zeta_{24})^+\)	None	✓	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{2}q^{5}+\beta _{1}q^{7}+2\beta _{2}q^{8}+\cdots\)
4563.2.a.w	$4563$	$2$	4563.a	1.a	$1$	$4$	$4$	$36.436$	4.4.8112.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
4563.2.a.x	$4563$	$2$	4563.a	1.a	$1$	$4$	$4$	$36.436$	4.4.8112.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
4563.2.a.y	$4563$	$2$	4563.a	1.a	$1$	$4$	$4$	$36.436$	4.4.8112.1	\(\Q(\sqrt{-39}) \)	✓	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots\)
4563.2.a.z	$4563$	$2$	4563.a	1.a	$1$	$4$	$4$	$36.436$	4.4.65712.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}-2q^{7}+\cdots\)
4563.2.a.ba	$4563$	$2$	4563.a	1.a	$1$	$4$	$4$	$36.436$	4.4.7600.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
4563.2.a.bb	$4563$	$2$	4563.a	1.a	$1$	$4$	$4$	$36.436$	4.4.8112.1	\(\Q(\sqrt{-39}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$3$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{2}+(4+\beta _{3})q^{4}-\beta _{2}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
4563.2.a.bc	$4563$	$2$	4563.a	1.a	$1$	$5$	$5$	$36.436$	5.5.4509957.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4563.2.a.bd	$4563$	$2$	4563.a	1.a	$1$	$5$	$5$	$36.436$	5.5.4509957.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(1+\beta _{4})q^{7}+\cdots\)
4563.2.a.be	$4563$	$2$	4563.a	1.a	$1$	$5$	$5$	$36.436$	5.5.4509957.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4563.2.a.bf	$4563$	$2$	4563.a	1.a	$1$	$5$	$5$	$36.436$	5.5.4509957.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}+(1+\beta _{4})q^{7}+\cdots\)
4563.2.a.bg	$4563$	$2$	4563.a	1.a	$1$	$6$	$6$	$36.436$	6.6.1997632.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots\)
4563.2.a.bh	$4563$	$2$	4563.a	1.a	$1$	$6$	$6$	$36.436$	6.6.1997632.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots\)
4563.2.a.bi	$4563$	$2$	4563.a	1.a	$1$	$6$	$6$	$36.436$	6.6.791844864.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4563.2.a.bj	$4563$	$2$	4563.a	1.a	$1$	$6$	$6$	$36.436$	6.6.791844864.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
4563.2.a.bk	$4563$	$2$	4563.a	1.a	$1$	$8$	$8$	$36.436$	8.8.\(\cdots\).1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4563.2.a.bl	$4563$	$2$	4563.a	1.a	$1$	$8$	$8$	$36.436$	8.8.\(\cdots\).1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4563.2.a.bm	$4563$	$2$	4563.a	1.a	$1$	$8$	$8$	$36.436$	8.8.\(\cdots\).6	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+(2-\beta _{4})q^{4}-\beta _{5}q^{5}+\beta _{2}q^{7}+\cdots\)
4563.2.a.bn	$4563$	$2$	4563.a	1.a	$1$	$12$	$12$	$36.436$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(0\)	\(-13\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
4563.2.a.bo	$4563$	$2$	4563.a	1.a	$1$	$12$	$12$	$36.436$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(0\)	\(-13\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
4563.2.a.bp	$4563$	$2$	4563.a	1.a	$1$	$12$	$12$	$36.436$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-14\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{11})q^{5}+\cdots\)
4563.2.a.bq	$4563$	$2$	4563.a	1.a	$1$	$12$	$12$	$36.436$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(14\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{11})q^{5}+\cdots\)
4563.2.a.br	$4563$	$2$	4563.a	1.a	$1$	$12$	$12$	$36.436$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(0\)	\(13\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
4563.2.a.bs	$4563$	$2$	4563.a	1.a	$1$	$12$	$12$	$36.436$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(0\)	\(13\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4563))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4563)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(351))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1521))\)\(^{\oplus 2}\)