Space of modular forms of level 6292, weight 2, and trivial character

• Label: 6292.2.a
• Level: $6292$
• Weight: $2$
• Character orbit: 6292.a
• Rep. character: $\chi_{6292}(1,\cdot)$
• Character field: $\Q$
• Dimension: $109$
• Newform subspaces: $26$
• Sturm bound: $1848$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 6292 = 2^{2} \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6292.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(1848\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6292))\).

	Total	New	Old
Modular forms	960	109	851
Cusp forms	889	109	780
Eisenstein series	71	0	71

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

\(2\)	\(11\)	\(13\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(29\)
\(-\)	\(+\)	\(-\)	$+$	\(25\)
\(-\)	\(-\)	\(+\)	$+$	\(25\)
\(-\)	\(-\)	\(-\)	$-$	\(30\)
Plus space			\(+\)	\(50\)
Minus space			\(-\)	\(59\)

Trace form

\( 109 q - 6 q^{5} + 2 q^{7} + 105 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6292))\) 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	11	13
6292.2.a.a	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-3\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}-4q^{7}+6q^{9}-q^{13}+\cdots\)
6292.2.a.b	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+4q^{7}+6q^{9}+q^{13}+\cdots\)
6292.2.a.c	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}-2q^{9}-q^{13}+5q^{17}+\cdots\)
6292.2.a.d	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}-2q^{9}+q^{13}-5q^{17}+\cdots\)
6292.2.a.e	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{9}-q^{13}-4q^{15}+\cdots\)
6292.2.a.f	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{9}+q^{13}-4q^{15}+\cdots\)
6292.2.a.g	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-3q^{9}+q^{13}-6q^{17}+\cdots\)
6292.2.a.h	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}-2q^{9}+q^{13}+3q^{17}+\cdots\)
6292.2.a.i	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}-2q^{9}-q^{13}-3q^{17}+\cdots\)
6292.2.a.j	$6292$	$2$	6292.a	1.a	$1$	$1$	$1$	$50.242$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-2q^{7}-2q^{9}-q^{13}+\cdots\)
6292.2.a.k	$6292$	$2$	6292.a	1.a	$1$	$2$	$2$	$50.242$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
6292.2.a.l	$6292$	$2$	6292.a	1.a	$1$	$2$	$2$	$50.242$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
6292.2.a.m	$6292$	$2$	6292.a	1.a	$1$	$2$	$2$	$50.242$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+(1+\beta )q^{7}+4q^{9}+\cdots\)
6292.2.a.n	$6292$	$2$	6292.a	1.a	$1$	$2$	$2$	$50.242$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+(-1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
6292.2.a.o	$6292$	$2$	6292.a	1.a	$1$	$2$	$2$	$50.242$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2q^{5}+(-3+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
6292.2.a.p	$6292$	$2$	6292.a	1.a	$1$	$3$	$3$	$50.242$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(2+2\beta _{1}+\cdots)q^{7}+\cdots\)
6292.2.a.q	$6292$	$2$	6292.a	1.a	$1$	$4$	$4$	$50.242$	4.4.725.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-6\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
6292.2.a.r	$6292$	$2$	6292.a	1.a	$1$	$4$	$4$	$50.242$	4.4.725.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(6\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
6292.2.a.s	$6292$	$2$	6292.a	1.a	$1$	$5$	$5$	$50.242$	5.5.223824.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}+(-\beta _{2}+\beta _{4})q^{9}+\cdots\)
6292.2.a.t	$6292$	$2$	6292.a	1.a	$1$	$5$	$5$	$50.242$	5.5.223824.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\beta _{4})q^{9}+\cdots\)
6292.2.a.u	$6292$	$2$	6292.a	1.a	$1$	$10$	$10$	$50.242$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{6})q^{5}-\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
6292.2.a.v	$6292$	$2$	6292.a	1.a	$1$	$10$	$10$	$50.242$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-6\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{6})q^{5}+\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
6292.2.a.w	$6292$	$2$	6292.a	1.a	$1$	$10$	$10$	$50.242$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-7\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{9})q^{5}+(-\beta _{1}+\beta _{8}+\cdots)q^{7}+\cdots\)
6292.2.a.x	$6292$	$2$	6292.a	1.a	$1$	$10$	$10$	$50.242$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-7\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{9})q^{5}+(\beta _{1}-\beta _{8}+\cdots)q^{7}+\cdots\)
6292.2.a.y	$6292$	$2$	6292.a	1.a	$1$	$14$	$14$	$50.242$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(9\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{11})q^{5}+(\beta _{5}-\beta _{8})q^{7}+\cdots\)
6292.2.a.z	$6292$	$2$	6292.a	1.a	$1$	$14$	$14$	$50.242$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(9\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{11})q^{5}+(-\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6292))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6292)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1573))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3146))\)\(^{\oplus 2}\)