Space of modular forms of level 42, weight 4, and Character 42.d

• Label: 42.4.d
• Level: $42$
• Weight: $4$
• Character orbit: 42.d
• Rep. character: $\chi_{42}(41,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	42.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(42, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	20	8	12
Eisenstein series	8	0	8

Trace form

8 * q - 32 * q^4 + 4 * q^7 - 60 * q^9 + 252 * q^15 + 128 * q^16 - 120 * q^18 - 168 * q^21 - 240 * q^22 + 320 * q^25 - 16 * q^28 + 312 * q^30 + 240 * q^36 - 592 * q^37 - 804 * q^39 - 216 * q^42 - 1696 * q^43 + 1344 * q^46 + 2192 * q^49 + 504 * q^51 + 2532 * q^57 - 1488 * q^58 - 1008 * q^60 - 2496 * q^63 - 512 * q^64 + 496 * q^67 - 192 * q^70 + 480 * q^72 + 1080 * q^78 + 2824 * q^79 + 672 * q^84 - 3936 * q^85 + 960 * q^88 - 264 * q^91 - 1512 * q^93 + 4032 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(42, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
42.4.d.a	$42$	$4$	42.d	21.c	$2$	$8$	$8$	$2.478$	8.0.\(\cdots\).13	None		✓	✓	✓	42.4.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{5}q^{3}-4q^{4}+(2\beta _{5}-2\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(42, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)