Space of modular forms of level 6192, weight 2, and Character 6192.l

• Label: 6192.2.l
• Level: $6192$
• Weight: $2$
• Character orbit: 6192.l
• Rep. character: $\chi_{6192}(2321,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $12$
• Sturm bound: $2112$
• Trace bound: $65$

Defining parameters

Level:	\( N \)	\(=\)	\( 6192 = 2^{4} \cdot 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6192.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2112\)
Trace bound:			\(65\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6192, [\chi])\).

	Total	New	Old
Modular forms	1080	88	992
Cusp forms	1032	88	944
Eisenstein series	48	0	48

Trace form

\( 88 q + 88 q^{25} - 8 q^{31} + 12 q^{43} - 72 q^{49} + 24 q^{67} - 40 q^{79} + 16 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6192, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6192.2.l.a	$6192$	$2$	6192.l	129.d	$2$	$2$	$2$	$49.443$	\(\Q(\sqrt{-2}) \)	None					3096.2.l.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}+\beta q^{11}+5\beta q^{17}+4\beta q^{19}+\cdots\)
6192.2.l.b	$6192$	$2$	6192.l	129.d	$2$	$2$	$2$	$49.443$	\(\Q(\sqrt{-2}) \)	None					3096.2.l.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}+2\beta q^{7}-\beta q^{11}+4q^{13}+\beta q^{17}+\cdots\)
6192.2.l.c	$6192$	$2$	6192.l	129.d	$2$	$2$	$2$	$49.443$	\(\Q(\sqrt{-2}) \)	None					3096.2.l.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}+\beta q^{11}+5\beta q^{17}-4\beta q^{19}+\cdots\)
6192.2.l.d	$6192$	$2$	6192.l	129.d	$2$	$2$	$2$	$49.443$	\(\Q(\sqrt{-2}) \)	None					3096.2.l.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-2\beta q^{7}-\beta q^{11}+4q^{13}+\beta q^{17}+\cdots\)
6192.2.l.e	$6192$	$2$	6192.l	129.d	$2$	$4$	$4$	$49.443$	\(\Q(\sqrt{-2}, \sqrt{43})\)	\(\Q(\sqrt{-43}) \)					387.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{11}+\beta _{3}q^{13}+(-\beta _{1}-\beta _{2})q^{17}+\cdots\)
6192.2.l.f	$6192$	$2$	6192.l	129.d	$2$	$6$	$6$	$49.443$	6.0.30233088.3	None					774.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}-\beta _{2}q^{7}+(\beta _{1}-\beta _{2})q^{11}+(2+\cdots)q^{13}+\cdots\)
6192.2.l.g	$6192$	$2$	6192.l	129.d	$2$	$6$	$6$	$49.443$	6.0.30233088.3	None					774.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}-\beta _{2}q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\cdots\)
6192.2.l.h	$6192$	$2$	6192.l	129.d	$2$	$8$	$8$	$49.443$	8.0.3588489216.5	None					1548.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+\beta _{6}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(-1+\cdots)q^{13}+\cdots\)
6192.2.l.i	$6192$	$2$	6192.l	129.d	$2$	$8$	$8$	$49.443$	\(\Q(\sqrt{-2}, \sqrt{3}, \sqrt{43})\)	\(\Q(\sqrt{-43}) \)					1548.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{11}-\beta _{1}q^{13}+\beta _{6}q^{17}+(-\beta _{3}+\cdots)q^{23}+\cdots\)
6192.2.l.j	$6192$	$2$	6192.l	129.d	$2$	$12$	$12$	$49.443$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					387.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{8}q^{7}+(-\beta _{4}-\beta _{10})q^{11}+\cdots\)
6192.2.l.k	$6192$	$2$	6192.l	129.d	$2$	$18$	$18$	$49.443$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					3096.2.l.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{13}q^{7}+\beta _{16}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
6192.2.l.l	$6192$	$2$	6192.l	129.d	$2$	$18$	$18$	$49.443$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					3096.2.l.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{13}q^{7}+\beta _{16}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(6192, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6192, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(258, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(387, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(516, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(774, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1032, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1548, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2064, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3096, [\chi])\)\(^{\oplus 2}\)