Space of modular forms of level 176, weight 2, and Character 176.m

• Label: 176.2.m
• Level: $176$
• Weight: $2$
• Character orbit: 176.m
• Rep. character: $\chi_{176}(49,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$176 = 2^{4} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	176.m (of order $5$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$11$
Character field:			$\Q(\zeta_{5})$
Newform subspaces:			$4$
Sturm bound:			$48$
Trace bound:			$3$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(176, [\chi])$.

	Total	New	Old
Modular forms	120	28	92
Cusp forms	72	20	52
Eisenstein series	48	8	40

Trace form

20 * q + 3 * q^3 - 3 * q^5 + q^7 - 10 * q^9 + 2 * q^11 - 3 * q^13 + 3 * q^15 - 7 * q^17 + 9 * q^19 - 2 * q^21 + 16 * q^23 - 12 * q^25 + 3 * q^27 + 5 * q^29 + 3 * q^31 + 5 * q^33 - 13 * q^35 - 15 * q^37 - 47 * q^39 + 13 * q^41 - 36 * q^43 + 8 * q^45 - 9 * q^47 + 2 * q^49 - 27 * q^51 - 23 * q^53 - 21 * q^55 + 13 * q^57 + 7 * q^59 - 11 * q^61 - 12 * q^63 - 6 * q^65 + 12 * q^67 - 28 * q^69 + 25 * q^71 - 3 * q^73 + 17 * q^75 + 15 * q^77 + 35 * q^79 + 28 * q^81 + 63 * q^83 + 31 * q^85 + 110 * q^87 - 4 * q^89 + 17 * q^91 + 11 * q^93 + 7 * q^95 + 19 * q^97 + 46 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(176, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.2.m.a	$176$	$2$	176.m	11.c	$5$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	None					88.2.i.a	$2$	$0$	$0$	$-3$	$3$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
176.2.m.b	$176$	$2$	176.m	11.c	$5$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	None					44.2.e.a	$2$	$0$	$0$	$1$	$3$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
176.2.m.c	$176$	$2$	176.m	11.c	$5$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	None					22.2.c.a	$2$	$0$	$0$	$4$	$-6$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots$
176.2.m.d	$176$	$2$	176.m	11.c	$5$	$8$	$2$	$1.405$	8.0.682515625.5	None			✓		88.2.i.b	$2$	$0$	$0$	$1$	$-3$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(176, [\chi])$ into lower level spaces

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