Space of modular forms of level 5292, weight 2, and trivial character

• Label: 5292.2.a
• Level: $5292$
• Weight: $2$
• Character orbit: 5292.a
• Rep. character: $\chi_{5292}(1,\cdot)$
• Character field: $\Q$
• Dimension: $55$
• Newform subspaces: $28$
• Sturm bound: $2016$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(2016\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5292))\).

	Total	New	Old
Modular forms	1080	55	1025
Cusp forms	937	55	882
Eisenstein series	143	0	143

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

\(2\)	\(3\)	\(7\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(14\)
\(-\)	\(+\)	\(-\)	$+$	\(13\)
\(-\)	\(-\)	\(+\)	$+$	\(13\)
\(-\)	\(-\)	\(-\)	$-$	\(15\)
Plus space			\(+\)	\(26\)
Minus space			\(-\)	\(29\)

Trace form

\( 55 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5292))\) 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	7
5292.2.a.a	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{13}-3q^{17}+4q^{19}+6q^{23}+\cdots\)
5292.2.a.b	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+3q^{11}-2q^{13}+6q^{17}-5q^{19}+\cdots\)
5292.2.a.c	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{11}-5q^{17}-2q^{19}+2q^{23}+\cdots\)
5292.2.a.d	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-7q^{13}+8q^{19}-5q^{25}+11q^{31}+\cdots\)
5292.2.a.e	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-5q^{13}-8q^{19}-5q^{25}+7q^{31}+\cdots\)
5292.2.a.f	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{13}+q^{19}-5q^{25}+7q^{31}-10q^{37}+\cdots\)
5292.2.a.g	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+2q^{13}-q^{19}-5q^{25}-7q^{31}-10q^{37}+\cdots\)
5292.2.a.h	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+5q^{13}+8q^{19}-5q^{25}-7q^{31}+\cdots\)
5292.2.a.i	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+7q^{13}-8q^{19}-5q^{25}-11q^{31}+\cdots\)
5292.2.a.j	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+7q^{13}+q^{19}-5q^{25}+4q^{31}-q^{37}+\cdots\)
5292.2.a.k	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{11}+5q^{17}-2q^{19}-2q^{23}+\cdots\)
5292.2.a.l	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-3q^{11}-2q^{13}-6q^{17}-5q^{19}+\cdots\)
5292.2.a.m	$5292$	$2$	5292.a	1.a	$1$	$1$	$1$	$42.257$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{13}+3q^{17}+4q^{19}-6q^{23}+\cdots\)
5292.2.a.n	$5292$	$2$	5292.a	1.a	$1$	$2$	$2$	$42.257$	\(\Q(\sqrt{7}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{11}-\beta q^{13}+3q^{17}-\beta q^{19}+\cdots\)
5292.2.a.o	$5292$	$2$	5292.a	1.a	$1$	$2$	$2$	$42.257$	\(\Q(\sqrt{13}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-\beta q^{11}-6q^{13}-2\beta q^{17}+\cdots\)
5292.2.a.p	$5292$	$2$	5292.a	1.a	$1$	$2$	$2$	$42.257$	\(\Q(\sqrt{7}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{11}-2q^{13}+q^{19}-3\beta q^{23}+\cdots\)
5292.2.a.q	$5292$	$2$	5292.a	1.a	$1$	$2$	$2$	$42.257$	\(\Q(\sqrt{10}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+2\beta q^{11}-\beta q^{17}-7q^{19}+\cdots\)
5292.2.a.r	$5292$	$2$	5292.a	1.a	$1$	$2$	$2$	$42.257$	\(\Q(\sqrt{10}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-2\beta q^{11}-\beta q^{17}+7q^{19}+\cdots\)
5292.2.a.s	$5292$	$2$	5292.a	1.a	$1$	$2$	$2$	$42.257$	\(\Q(\sqrt{7}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+\beta q^{11}+2q^{13}-q^{19}+3\beta q^{23}+\cdots\)
5292.2.a.t	$5292$	$2$	5292.a	1.a	$1$	$2$	$2$	$42.257$	\(\Q(\sqrt{7}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{11}-\beta q^{13}-3q^{17}-\beta q^{19}+\cdots\)
5292.2.a.u	$5292$	$2$	5292.a	1.a	$1$	$3$	$3$	$42.257$	3.3.321.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(-2+\beta _{1})q^{11}+(-1-\beta _{2})q^{13}+\cdots\)
5292.2.a.v	$5292$	$2$	5292.a	1.a	$1$	$3$	$3$	$42.257$	3.3.321.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(2-\beta _{1})q^{11}+(1+\beta _{2})q^{13}+\cdots\)
5292.2.a.w	$5292$	$2$	5292.a	1.a	$1$	$3$	$3$	$42.257$	3.3.321.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(-2+\beta _{1})q^{11}+(1+\beta _{2})q^{13}+\cdots\)
5292.2.a.x	$5292$	$2$	5292.a	1.a	$1$	$3$	$3$	$42.257$	3.3.321.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(2-\beta _{1})q^{11}+(-1-\beta _{2})q^{13}+\cdots\)
5292.2.a.y	$5292$	$2$	5292.a	1.a	$1$	$4$	$4$	$42.257$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{11}+3\beta _{1}q^{13}+\cdots\)
5292.2.a.z	$5292$	$2$	5292.a	1.a	$1$	$4$	$4$	$42.257$	4.4.7168.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{5}+(2\beta _{1}+\beta _{3})q^{11}+(-3\beta _{1}+\cdots)q^{17}+\cdots\)
5292.2.a.ba	$5292$	$2$	5292.a	1.a	$1$	$4$	$4$	$42.257$	4.4.7168.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{5}+(-2\beta _{1}-\beta _{3})q^{11}+(-3\beta _{1}+\cdots)q^{17}+\cdots\)
5292.2.a.bb	$5292$	$2$	5292.a	1.a	$1$	$4$	$4$	$42.257$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{11}-3\beta _{1}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5292))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5292)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(756))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1323))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1764))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2646))\)\(^{\oplus 2}\)