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

• Label: 6192.2.d
• Level: $6192$
• Weight: $2$
• Character orbit: 6192.d
• Rep. character: $\chi_{6192}(431,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $5$
• Sturm bound: $2112$
• Trace bound: $11$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	1080	84	996
Cusp forms	1032	84	948
Eisenstein series	48	0	48

Trace form

\( 84 q - 36 q^{25} - 24 q^{37} - 132 q^{49} + 24 q^{61} - 48 q^{73} - 72 q^{85} + 48 q^{97}+O(q^{100}) \)

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.d.a	$6192$	$2$	6192.d	12.b	$2$	$4$	$4$	$49.443$	\(\Q(\zeta_{8})\)	None		✓			6192.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta_1 q^{5}+(\beta_{2}-\beta_1)q^{7}+(\beta_{3}-5)q^{11}+\cdots\)
6192.2.d.b	$6192$	$2$	6192.d	12.b	$2$	$4$	$4$	$49.443$	\(\Q(\zeta_{8})\)	None		✓			6192.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}-4\beta_1 q^{7}-2\beta_{3} q^{11}+4 q^{13}+\cdots\)
6192.2.d.c	$6192$	$2$	6192.d	12.b	$2$	$4$	$4$	$49.443$	\(\Q(\zeta_{8})\)	None		✓			6192.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta_1 q^{5}+(-\beta_{2}+\beta_1)q^{7}+(-\beta_{3}+5)q^{11}+\cdots\)
6192.2.d.d	$6192$	$2$	6192.d	12.b	$2$	$16$	$16$	$49.443$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			6192.2.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{8}-\beta _{10})q^{5}+(-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
6192.2.d.e	$6192$	$2$	6192.d	12.b	$2$	$56$	$56$	$49.443$		None		✓	✓		6192.2.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(6192, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(516, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1548, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2064, [\chi])\)\(^{\oplus 2}\)