Space of modular forms of level 158, weight 4, and Character 158.c

• Label: 158.4.c
• Level: $158$
• Weight: $4$
• Character orbit: 158.c
• Rep. character: $\chi_{158}(23,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	158.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(158, [\chi])\).

	Total	New	Old
Modular forms	124	40	84
Cusp forms	116	40	76
Eisenstein series	8	0	8

Trace form

40 * q + 6 * q^3 - 80 * q^4 + 12 * q^6 - 22 * q^7 - 212 * q^9 - 24 * q^10 + 56 * q^11 - 48 * q^12 - 54 * q^13 - 112 * q^14 + 92 * q^15 - 320 * q^16 - 360 * q^17 + 80 * q^18 - 64 * q^19 - 16 * q^21 - 168 * q^22 + 16 * q^23 + 48 * q^24 - 414 * q^25 - 80 * q^26 - 1320 * q^27 - 88 * q^28 + 606 * q^29 + 100 * q^30 - 18 * q^31 - 512 * q^33 + 160 * q^34 + 588 * q^35 - 848 * q^36 + 676 * q^37 - 600 * q^38 + 342 * q^39 + 48 * q^40 - 684 * q^41 + 108 * q^42 + 518 * q^43 + 224 * q^44 + 338 * q^45 - 224 * q^46 - 66 * q^47 + 96 * q^48 + 506 * q^49 + 320 * q^50 + 1196 * q^51 + 432 * q^52 - 392 * q^53 - 420 * q^54 + 486 * q^55 + 224 * q^56 - 2348 * q^57 + 536 * q^58 + 588 * q^59 - 184 * q^60 + 1204 * q^61 + 488 * q^62 - 2138 * q^63 + 2560 * q^64 + 392 * q^65 - 864 * q^66 + 2160 * q^67 + 720 * q^68 + 3832 * q^69 - 1656 * q^70 + 3296 * q^71 - 160 * q^72 + 1542 * q^73 + 488 * q^74 + 1344 * q^75 - 256 * q^76 + 1456 * q^77 - 3656 * q^78 + 2922 * q^79 - 704 * q^81 + 448 * q^82 - 712 * q^83 + 32 * q^84 + 2524 * q^85 + 908 * q^86 - 4064 * q^87 + 336 * q^88 - 4076 * q^89 + 1060 * q^90 - 2620 * q^91 + 64 * q^92 + 1192 * q^93 + 2504 * q^94 + 2428 * q^95 - 384 * q^96 + 4688 * q^97 - 1560 * q^98 + 3906 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(158, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
158.4.c.a	$158$	$4$	158.c	79.c	$3$	$20$	$10$	$9.322$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			158.4.c.a	$2$	$0$	\(-20\)	\(6\)	\(3\)	\(3\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\beta _{2})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
158.4.c.b	$158$	$4$	158.c	79.c	$3$	$20$	$10$	$9.322$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			158.4.c.b	$2$	$0$	\(20\)	\(0\)	\(-3\)	\(-25\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{2}-\beta _{1}q^{3}+(-4-4\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(158, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(158, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)