Space of modular forms of level 4840, weight 2, and trivial character

• Label: 4840.2.a
• Level: $4840$
• Weight: $2$
• Character orbit: 4840.a
• Rep. character: $\chi_{4840}(1,\cdot)$
• Character field: $\Q$
• Dimension: $109$
• Newform subspaces: $34$
• Sturm bound: $1584$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4840.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 34 \)
Sturm bound:			\(1584\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4840))\).

	Total	New	Old
Modular forms	840	109	731
Cusp forms	745	109	636
Eisenstein series	95	0	95

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

\(2\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(102\)	\(12\)	\(90\)		\(91\)	\(12\)	\(79\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(107\)	\(15\)	\(92\)		\(95\)	\(15\)	\(80\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(108\)	\(17\)	\(91\)		\(96\)	\(17\)	\(79\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(103\)	\(10\)	\(93\)		\(91\)	\(10\)	\(81\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(108\)	\(12\)	\(96\)		\(96\)	\(12\)	\(84\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(103\)	\(15\)	\(88\)		\(91\)	\(15\)	\(76\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(102\)	\(13\)	\(89\)		\(90\)	\(13\)	\(77\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(107\)	\(15\)	\(92\)		\(95\)	\(15\)	\(80\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(410\)	\(50\)	\(360\)		\(363\)	\(50\)	\(313\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(430\)	\(59\)	\(371\)		\(382\)	\(59\)	\(323\)		\(48\)	\(0\)	\(48\)

Trace form

109 * q - 4 * q^3 + q^5 - 4 * q^7 + 117 * q^9 - 6 * q^13 - 2 * q^17 - 12 * q^19 - 16 * q^21 - 4 * q^23 + 109 * q^25 - 16 * q^27 - 10 * q^29 - 24 * q^31 + 4 * q^35 - 10 * q^37 + 16 * q^39 + 18 * q^41 - 8 * q^43 - 3 * q^45 + 20 * q^47 + 105 * q^49 + 16 * q^51 + 14 * q^53 + 16 * q^57 + 12 * q^59 + 6 * q^61 - 20 * q^63 + 2 * q^65 - 4 * q^67 + 16 * q^69 - 16 * q^71 + 6 * q^73 - 4 * q^75 + 16 * q^79 + 101 * q^81 + 16 * q^83 - 2 * q^85 + 40 * q^87 + 18 * q^89 - 16 * q^91 + 4 * q^95 + 30 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4840))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	5	11
4840.2.a.a	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓	✓			4840.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
4840.2.a.b	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓	✓			4840.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
4840.2.a.c	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓				440.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}+8q^{19}-8q^{23}+\cdots\)
4840.2.a.d	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓				440.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}+4q^{13}+4q^{17}+\cdots\)
4840.2.a.e	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓				440.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-3q^{9}-6q^{13}+6q^{17}+\cdots\)
4840.2.a.f	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓				40.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-3q^{9}+2q^{13}-2q^{17}+\cdots\)
4840.2.a.g	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓	✓			4840.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}-2q^{9}+4q^{13}+\cdots\)
4840.2.a.h	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓	✓			4840.2.a.g	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}-2q^{9}-4q^{13}+\cdots\)
4840.2.a.i	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	\(\Q\)	None	✓				440.2.a.d	$1$	$0$	\(0\)	\(3\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}-q^{7}+6q^{9}+6q^{13}+\cdots\)
4840.2.a.j	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-2q^{13}+\cdots\)
4840.2.a.k	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	\(\Q(\sqrt{3}) \)	None	✓	✓			4840.2.a.k	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(-2-\beta )q^{7}+2\beta q^{13}+\cdots\)
4840.2.a.l	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	\(\Q(\sqrt{3}) \)	None	✓	✓			4840.2.a.k	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(2+\beta )q^{7}-2\beta q^{13}+\cdots\)
4840.2.a.m	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
4840.2.a.n	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.f	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
4840.2.a.o	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	\(\Q(\sqrt{2}) \)	None	✓	✓			4840.2.a.o	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+2\beta q^{9}+\cdots\)
4840.2.a.p	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	\(\Q(\sqrt{2}) \)	None	✓	✓			4840.2.a.o	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(1+\beta )q^{7}+2\beta q^{9}+\cdots\)
4840.2.a.q	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.568.1	None	✓	✓			4840.2.a.q	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
4840.2.a.r	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.568.1	None	✓	✓			4840.2.a.q	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
4840.2.a.s	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.788.1	None	✓	✓			4840.2.a.s	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
4840.2.a.t	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.404.1	None	✓	✓			4840.2.a.t	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
4840.2.a.u	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.404.1	None	✓	✓			4840.2.a.t	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
4840.2.a.v	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.788.1	None	✓	✓			4840.2.a.s	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
4840.2.a.w	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.4752.1	None	✓	✓			4840.2.a.w	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(-2-\beta _{2}+\beta _{3})q^{7}+\cdots\)
4840.2.a.x	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.4752.1	None	✓	✓			4840.2.a.w	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(6\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(2+\beta _{2}-\beta _{3})q^{7}+\cdots\)
4840.2.a.y	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.725.1	None	✓				440.2.y.a	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
4840.2.a.z	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.725.1	None	✓		✓		440.2.y.a	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
4840.2.a.ba	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.25903625.1	None	✓		✓		440.2.y.c	$1$	$1$	\(0\)	\(-3\)	\(-6\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
4840.2.a.bb	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.25903625.1	None	✓		✓		440.2.y.c	$1$	$1$	\(0\)	\(-3\)	\(-6\)	\(7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots\)
4840.2.a.bc	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.22733568.1	None	✓	✓	✓		4840.2.a.bc	$1$	$1$	\(0\)	\(-2\)	\(6\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
4840.2.a.bd	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.22733568.1	None	✓	✓			4840.2.a.bc	$1$	$0$	\(0\)	\(-2\)	\(6\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(\beta _{3}+\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
4840.2.a.be	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.45753625.1	None	✓		✓		440.2.y.b	$1$	$0$	\(0\)	\(2\)	\(-6\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-q^{5}+(-1+\beta _{2}+\beta _{5})q^{7}+\cdots\)
4840.2.a.bf	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.45753625.1	None	✓		✓		440.2.y.b	$1$	$0$	\(0\)	\(2\)	\(-6\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-q^{5}+(1-\beta _{2}-\beta _{5})q^{7}+(-2\beta _{2}+\cdots)q^{9}+\cdots\)
4840.2.a.bg	$4840$	$2$	4840.a	1.a	$1$	$8$	$8$	$38.648$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		440.2.y.d	$1$	$0$	\(0\)	\(1\)	\(8\)	\(-6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)
4840.2.a.bh	$4840$	$2$	4840.a	1.a	$1$	$8$	$8$	$38.648$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		440.2.y.d	$1$	$0$	\(0\)	\(1\)	\(8\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4840)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\)\(^{\oplus 2}\)