Space of modular forms of level 4620, weight 2, and trivial character

• Label: 4620.2.a
• Level: $4620$
• Weight: $2$
• Character orbit: 4620.a
• Rep. character: $\chi_{4620}(1,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $24$
• Sturm bound: $2304$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 4620 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4620.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(2304\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4620))\).

	Total	New	Old
Modular forms	1176	40	1136
Cusp forms	1129	40	1089
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(5\)	\(7\)	\(11\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	$-$	\(4\)
Plus space					\(+\)	\(16\)
Minus space					\(-\)	\(24\)

Trace form

\( 40 q + 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4620))\) 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	11
4620.2.a.a	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4620.2.a.b	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
4620.2.a.c	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
4620.2.a.d	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
4620.2.a.e	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
4620.2.a.f	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
4620.2.a.g	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
4620.2.a.h	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{15}+\cdots\)
4620.2.a.i	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{15}+\cdots\)
4620.2.a.j	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
4620.2.a.k	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
4620.2.a.l	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4620.2.a.m	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+q^{15}+\cdots\)
4620.2.a.n	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
4620.2.a.o	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+(-3+\cdots)q^{13}+\cdots\)
4620.2.a.p	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
4620.2.a.q	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
4620.2.a.r	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(2+\beta )q^{13}+\cdots\)
4620.2.a.s	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+(-5+\cdots)q^{13}+\cdots\)
4620.2.a.t	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.1944.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-\beta _{2}q^{13}+\cdots\)
4620.2.a.u	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.8220.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
4620.2.a.v	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots\)
4620.2.a.w	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.3576.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
4620.2.a.x	$4620$	$2$	4620.a	1.a	$1$	$4$	$4$	$36.891$	4.4.138892.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+(1+\beta _{3})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4620))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4620)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\)\(^{\oplus 2}\)