Space of modular forms of level 192, weight 4, and Character 192.c

• Label: 192.4.c
• Level: $192$
• Weight: $4$
• Character orbit: 192.c
• Rep. character: $\chi_{192}(191,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).

	Total	New	Old
Modular forms	108	26	82
Cusp forms	84	22	62
Eisenstein series	24	4	20

Trace form

\( 22 q - 2 q^{9} - 68 q^{13} - 52 q^{21} - 354 q^{25} + 176 q^{33} - 500 q^{37} + 736 q^{45} - 494 q^{49} + 396 q^{57} - 164 q^{61} + 800 q^{69} - 4 q^{73} + 2150 q^{81} - 256 q^{85} + 284 q^{93} - 1492 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(192, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.4.c.a	$192$	$4$	192.c	12.b	$2$	$2$	$2$	$11.328$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					48.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}-6\beta q^{7}-27 q^{9}-70 q^{13}+\cdots\)
192.4.c.b	$192$	$4$	192.c	12.b	$2$	$4$	$4$	$11.328$	\(\Q(\sqrt{3}, \sqrt{-5})\)	None					12.4.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\)
192.4.c.c	$192$	$4$	192.c	12.b	$2$	$4$	$4$	$11.328$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					48.4.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}-5\beta _{1}q^{7}+(21-\beta _{3})q^{9}+\cdots\)
192.4.c.d	$192$	$4$	192.c	12.b	$2$	$12$	$12$	$11.328$	12.0.\(\cdots\).1	None			✓		96.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{44}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+\beta _{8}q^{5}+\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)