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

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