Space of modular forms of level 192, weight 2, and Character 192.k

• Label: 192.2.k
• Level: $192$
• Weight: $2$
• Character orbit: 192.k
• Rep. character: $\chi_{192}(47,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(192, [\chi])\).

	Total	New	Old
Modular forms	80	20	60
Cusp forms	48	12	36
Eisenstein series	32	8	24

Trace form

12 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 + 12 * q^19 - 8 * q^21 - 10 * q^27 - 4 * q^33 - 4 * q^37 - 20 * q^39 - 12 * q^43 - 12 * q^45 - 20 * q^49 - 24 * q^51 - 24 * q^55 + 12 * q^61 - 28 * q^67 + 4 * q^69 + 34 * q^75 - 4 * q^81 + 32 * q^85 + 60 * q^87 + 56 * q^91 + 28 * q^93 - 8 * q^97 + 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(192, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.2.k.a	$192$	$2$	192.k	48.k	$4$	$12$	$6$	$1.533$	12.0.\(\cdots\).2	None			✓	✓	48.2.k.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(8\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{10}q^{3}+\beta _{7}q^{5}+(1-\beta _{11})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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