Space of modular forms of level 176, weight 4, and Character 176.m

• Label: 176.4.m
• Level: $176$
• Weight: $4$
• Character orbit: 176.m
• Rep. character: $\chi_{176}(49,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $68$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$176 = 2^{4} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	176.m (of order $5$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$11$
Character field:			$\Q(\zeta_{5})$
Newform subspaces:			$6$
Sturm bound:			$96$
Trace bound:			$3$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(176, [\chi])$.

	Total	New	Old
Modular forms	312	76	236
Cusp forms	264	68	196
Eisenstein series	48	8	40

Trace form

68 * q + 3 * q^3 - 3 * q^5 + 17 * q^7 - 118 * q^9 - 6 * q^11 - 3 * q^13 - 45 * q^15 - 79 * q^17 - 111 * q^19 + 46 * q^21 - 240 * q^23 - 160 * q^25 + 171 * q^27 - 203 * q^29 + 3 * q^31 + 489 * q^33 - 1189 * q^35 + 9 * q^37 + 1089 * q^39 - 467 * q^41 + 1068 * q^43 + 296 * q^45 + 1143 * q^47 - 1106 * q^49 - 1131 * q^51 - 175 * q^53 - 2797 * q^55 + 1057 * q^57 + 407 * q^59 + 197 * q^61 + 28 * q^63 - 38 * q^65 + 956 * q^67 + 956 * q^69 + 2921 * q^71 + 2301 * q^73 + 2441 * q^75 + 1511 * q^77 + 1123 * q^79 - 1028 * q^81 - 1425 * q^83 - 1697 * q^85 - 5410 * q^87 - 3164 * q^89 - 3807 * q^91 - 1429 * q^93 + 343 * q^95 - 449 * q^97 + 3630 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(176, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.4.m.a	$176$	$4$	176.m	11.c	$5$	$4$	$1$	$10.384$	$\Q(\zeta_{10})$	None					22.4.c.a	$2$	$0$	$0$	$1$	$3$	$-25$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(3\zeta_{10}+5\zeta_{10}^{2}+3\zeta_{10}^{3})q^{3}+(1+\cdots)q^{5}+\cdots$
176.4.m.b	$176$	$4$	176.m	11.c	$5$	$8$	$2$	$10.384$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					22.4.c.b	$2$	$0$	$0$	$-3$	$5$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(-5-8\beta _{2}+\cdots)q^{5}+\cdots$
176.4.m.c	$176$	$4$	176.m	11.c	$5$	$8$	$2$	$10.384$	8.0.$\cdots$.1	None					11.4.c.a	$2$	$0$	$0$	$3$	$-7$	$35$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{2}+\beta _{4}+\beta _{5}+\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{5}+\cdots$
176.4.m.d	$176$	$4$	176.m	11.c	$5$	$12$	$3$	$10.384$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					44.4.e.a	$2$	$0$	$0$	$4$	$-4$	$-6$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{3}+(1+\beta _{1}+3\beta _{2}+3\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
176.4.m.e	$176$	$4$	176.m	11.c	$5$	$16$	$4$	$10.384$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					88.4.i.a	$2$	$0$	$0$	$1$	$-1$	$13$	$2^{12}$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{3}+2\beta _{5}+\beta _{13}+\cdots)q^{5}+\cdots$
176.4.m.f	$176$	$4$	176.m	11.c	$5$	$20$	$5$	$10.384$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None			✓		88.4.i.b	$2$	$0$	$0$	$-3$	$1$	$-1$	$2^{16}\cdot 5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{6}-\beta _{7}-\beta _{9})q^{3}+(1+\beta _{3}+\cdots)q^{5}+\cdots$

Decomposition of $S_{4}^{\mathrm{old}}(176, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(176, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(11, [\chi])$$^{\oplus 5}$$\oplus$$S_{4}^{\mathrm{new}}(22, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(44, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(88, [\chi])$$^{\oplus 2}$