Space of modular forms of level 4842, weight 2, and trivial character

• Label: 4842.2.a
• Level: $4842$
• Weight: $2$
• Character orbit: 4842.a
• Rep. character: $\chi_{4842}(1,\cdot)$
• Character field: $\Q$
• Dimension: $113$
• Newform subspaces: $21$
• Sturm bound: $1620$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4842 = 2 \cdot 3^{2} \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4842.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1620\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4842))\).

	Total	New	Old
Modular forms	818	113	705
Cusp forms	803	113	690
Eisenstein series	15	0	15

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

\(2\)	\(3\)	\(269\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(14\)
\(+\)	\(-\)	\(+\)	\(-\)	\(15\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(14\)
\(-\)	\(+\)	\(-\)	\(+\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(13\)
\(-\)	\(-\)	\(-\)	\(-\)	\(21\)
Plus space			\(+\)	\(49\)
Minus space			\(-\)	\(64\)

Trace form

113 * q + q^2 + 113 * q^4 - 4 * q^5 - 4 * q^7 + q^8 - 2 * q^10 + 2 * q^11 - 4 * q^14 + 113 * q^16 + 14 * q^17 - 4 * q^19 - 4 * q^20 - 8 * q^22 - 4 * q^23 + 109 * q^25 + 6 * q^26 - 4 * q^28 + 18 * q^29 + 12 * q^31 + q^32 + 2 * q^34 - 4 * q^35 + 12 * q^37 + 10 * q^38 - 2 * q^40 + 10 * q^41 + 2 * q^43 + 2 * q^44 - 8 * q^47 + 137 * q^49 - q^50 - 12 * q^53 + 4 * q^55 - 4 * q^56 + 12 * q^58 + 44 * q^59 + 28 * q^61 + 4 * q^62 + 113 * q^64 + 28 * q^65 - 2 * q^67 + 14 * q^68 + 16 * q^70 - 12 * q^71 + 26 * q^73 + 6 * q^74 - 4 * q^76 + 4 * q^77 + 24 * q^79 - 4 * q^80 - 10 * q^82 + 52 * q^83 - 4 * q^85 + 20 * q^86 - 8 * q^88 - 38 * q^89 - 28 * q^91 - 4 * q^92 - 4 * q^94 - 8 * q^95 + 22 * q^97 - 7 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4842))\) 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	3	269
4842.2.a.a	$4842$	$2$	4842.a	1.a	$1$	$1$	$1$	$38.664$	\(\Q\)	None	✓	✓			4842.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+2q^{7}-q^{8}-2q^{10}+\cdots\)
4842.2.a.b	$4842$	$2$	4842.a	1.a	$1$	$1$	$1$	$38.664$	\(\Q\)	None	✓				1614.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-2q^{10}+\cdots\)
4842.2.a.c	$4842$	$2$	4842.a	1.a	$1$	$1$	$1$	$38.664$	\(\Q\)	None	✓	✓			4842.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots\)
4842.2.a.d	$4842$	$2$	4842.a	1.a	$1$	$2$	$2$	$38.664$	\(\Q(\sqrt{13}) \)	None	✓				538.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots\)
4842.2.a.e	$4842$	$2$	4842.a	1.a	$1$	$2$	$2$	$38.664$	\(\Q(\sqrt{5}) \)	None	✓				1614.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2\beta q^{5}+(-1+3\beta )q^{7}+\cdots\)
4842.2.a.f	$4842$	$2$	4842.a	1.a	$1$	$2$	$2$	$38.664$	\(\Q(\sqrt{5}) \)	None	✓				538.2.a.a	$1$	$0$	\(-2\)	\(0\)	\(5\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(3-\beta )q^{5}+(-3+2\beta )q^{7}+\cdots\)
4842.2.a.g	$4842$	$2$	4842.a	1.a	$1$	$3$	$3$	$38.664$	3.3.361.1	None	✓				1614.2.a.d	$1$	$0$	\(-3\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1-\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4842.2.a.h	$4842$	$2$	4842.a	1.a	$1$	$3$	$3$	$38.664$	\(\Q(\zeta_{14})^+\)	None	✓				1614.2.a.e	$1$	$1$	\(-3\)	\(0\)	\(7\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
4842.2.a.i	$4842$	$2$	4842.a	1.a	$1$	$3$	$3$	$38.664$	\(\Q(\zeta_{14})^+\)	None	✓				1614.2.a.c	$1$	$1$	\(3\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
4842.2.a.j	$4842$	$2$	4842.a	1.a	$1$	$4$	$4$	$38.664$	4.4.4913.1	None	✓				538.2.a.c	$1$	$1$	\(4\)	\(0\)	\(-5\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+\cdots\)
4842.2.a.k	$4842$	$2$	4842.a	1.a	$1$	$5$	$5$	$38.664$	5.5.459533.1	None	✓				1614.2.a.f	$1$	$0$	\(5\)	\(0\)	\(5\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
4842.2.a.l	$4842$	$2$	4842.a	1.a	$1$	$6$	$6$	$38.664$	6.6.20228249.1	None	✓				1614.2.a.h	$1$	$1$	\(-6\)	\(0\)	\(-6\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
4842.2.a.m	$4842$	$2$	4842.a	1.a	$1$	$6$	$6$	$38.664$	6.6.137144153.1	None	✓		✓		1614.2.a.g	$1$	$1$	\(6\)	\(0\)	\(-6\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
4842.2.a.n	$4842$	$2$	4842.a	1.a	$1$	$7$	$7$	$38.664$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		538.2.a.e	$1$	$1$	\(-7\)	\(0\)	\(-7\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta _{4})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
4842.2.a.o	$4842$	$2$	4842.a	1.a	$1$	$7$	$7$	$38.664$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				538.2.a.d	$1$	$0$	\(7\)	\(0\)	\(6\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-\beta _{3}+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4842.2.a.p	$4842$	$2$	4842.a	1.a	$1$	$8$	$8$	$38.664$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		1614.2.a.j	$1$	$0$	\(-8\)	\(0\)	\(-4\)	\(9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
4842.2.a.q	$4842$	$2$	4842.a	1.a	$1$	$8$	$8$	$38.664$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		1614.2.a.i	$1$	$0$	\(8\)	\(0\)	\(0\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{8}+\cdots\)
4842.2.a.r	$4842$	$2$	4842.a	1.a	$1$	$9$	$9$	$38.664$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	4842.2.a.r	$1$	$1$	\(-9\)	\(0\)	\(5\)	\(-10\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1-\beta _{1})q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots\)
4842.2.a.s	$4842$	$2$	4842.a	1.a	$1$	$9$	$9$	$38.664$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	4842.2.a.r	$1$	$1$	\(9\)	\(0\)	\(-5\)	\(-10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots\)
4842.2.a.t	$4842$	$2$	4842.a	1.a	$1$	$13$	$13$	$38.664$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓		4842.2.a.t	$1$	$0$	\(-13\)	\(0\)	\(-5\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}-q^{8}+\cdots\)
4842.2.a.u	$4842$	$2$	4842.a	1.a	$1$	$13$	$13$	$38.664$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓		4842.2.a.t	$1$	$0$	\(13\)	\(0\)	\(5\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4842))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4842)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(269))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(538))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(807))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1614))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2421))\)\(^{\oplus 2}\)