Space of modular forms of level 2520, weight 2, and trivial character

• Label: 2520.2.a
• Level: $2520$
• Weight: $2$
• Character orbit: 2520.a
• Rep. character: $\chi_{2520}(1,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $25$
• Sturm bound: $1152$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(1152\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2520))\).

	Total	New	Old
Modular forms	608	30	578
Cusp forms	545	30	515
Eisenstein series	63	0	63

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

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(1\)
Plus space				\(+\)	\(12\)
Minus space				\(-\)	\(18\)

Trace form

\( 30 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2520))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	7
2520.2.a.a	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
2520.2.a.b	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-4q^{11}+6q^{13}+4q^{17}+\cdots\)
2520.2.a.c	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-2q^{11}-2q^{13}+6q^{17}+\cdots\)
2520.2.a.d	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{13}-2q^{17}+q^{25}+\cdots\)
2520.2.a.e	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{11}-6q^{13}-2q^{17}+\cdots\)
2520.2.a.f	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
2520.2.a.g	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
2520.2.a.h	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+2q^{11}-2q^{13}-2q^{17}+\cdots\)
2520.2.a.i	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+5q^{11}-5q^{13}+7q^{17}+\cdots\)
2520.2.a.j	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
2520.2.a.k	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{11}-6q^{13}+2q^{17}+\cdots\)
2520.2.a.l	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
2520.2.a.m	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{11}-2q^{13}-6q^{17}+\cdots\)
2520.2.a.n	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+4q^{11}-6q^{13}+2q^{17}+\cdots\)
2520.2.a.o	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+4q^{11}+6q^{13}-4q^{17}+\cdots\)
2520.2.a.p	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+5q^{11}+q^{13}-3q^{17}+\cdots\)
2520.2.a.q	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
2520.2.a.r	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
2520.2.a.s	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
2520.2.a.t	$2520$	$2$	2520.a	1.a	$1$	$1$	$1$	$20.122$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
2520.2.a.u	$2520$	$2$	2520.a	1.a	$1$	$2$	$2$	$20.122$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+(-1-\beta )q^{11}+2q^{13}+\cdots\)
2520.2.a.v	$2520$	$2$	2520.a	1.a	$1$	$2$	$2$	$20.122$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
2520.2.a.w	$2520$	$2$	2520.a	1.a	$1$	$2$	$2$	$20.122$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
2520.2.a.x	$2520$	$2$	2520.a	1.a	$1$	$2$	$2$	$20.122$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+(-3-\beta )q^{11}+(1+\beta )q^{13}+\cdots\)
2520.2.a.y	$2520$	$2$	2520.a	1.a	$1$	$2$	$2$	$20.122$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+(1+\beta )q^{11}+2q^{13}+(1+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1260))\)\(^{\oplus 2}\)