Space of modular forms of level 722, weight 2, and Character 722.c

• Label: 722.2.c
• Level: $722$
• Weight: $2$
• Character orbit: 722.c
• Rep. character: $\chi_{722}(429,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $54$
• Newform subspaces: $14$
• Sturm bound: $190$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(190\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(722, [\chi])\).

	Total	New	Old
Modular forms	230	54	176
Cusp forms	150	54	96
Eisenstein series	80	0	80

Trace form

54 * q + q^2 + q^3 - 27 * q^4 + 4 * q^5 - q^6 - 2 * q^8 - 24 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 6 * q^13 + 6 * q^14 - 14 * q^15 - 27 * q^16 - 4 * q^17 - 20 * q^18 - 8 * q^20 + 10 * q^21 - 7 * q^22 - 2 * q^23 - q^24 - 27 * q^25 - 4 * q^26 + 10 * q^27 - 2 * q^29 + 28 * q^30 + 8 * q^31 + q^32 - 11 * q^33 + 6 * q^34 - 8 * q^35 - 24 * q^36 + 8 * q^37 - 16 * q^39 + 2 * q^40 + 19 * q^41 + 24 * q^42 + 18 * q^43 + q^44 - 36 * q^45 - 16 * q^46 + 22 * q^47 + q^48 + 18 * q^49 - 22 * q^50 - 6 * q^51 + 6 * q^52 + 2 * q^53 + 11 * q^54 + 22 * q^55 - 12 * q^56 - 4 * q^58 - 9 * q^59 - 14 * q^60 - 12 * q^61 - 8 * q^62 + 32 * q^63 + 54 * q^64 - 8 * q^65 - 13 * q^66 - 11 * q^67 + 8 * q^68 + 40 * q^69 - 12 * q^70 - 22 * q^71 + 10 * q^72 + 27 * q^73 + 22 * q^74 + 66 * q^75 + 52 * q^77 - 2 * q^78 - 12 * q^79 + 4 * q^80 - 31 * q^81 + 5 * q^82 - 26 * q^83 - 20 * q^84 + 12 * q^85 + 16 * q^86 - 56 * q^87 + 14 * q^88 + 6 * q^89 + 8 * q^90 - 4 * q^91 - 2 * q^92 - 28 * q^94 + 2 * q^96 - q^97 - 7 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(722, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
722.2.c.a	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	\(\Q(\sqrt{-3}) \)	None		✓			722.2.a.a	$2$	$1$	\(-1\)	\(-3\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.b	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	\(\Q(\sqrt{-3}) \)	None					38.2.c.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.c	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	\(\Q(\sqrt{-3}) \)	None					38.2.a.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.d	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	\(\Q(\sqrt{-3}) \)	None					38.2.a.b	$2$	$0$	\(-1\)	\(1\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.e	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	\(\Q(\sqrt{-3}) \)	None					38.2.a.a	$2$	$1$	\(1\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.f	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	\(\Q(\sqrt{-3}) \)	None					38.2.a.b	$2$	$0$	\(1\)	\(-1\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.g	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	\(\Q(\sqrt{-3}) \)	None		✓			722.2.a.a	$2$	$0$	\(1\)	\(3\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.h	$722$	$2$	722.c	19.c	$3$	$4$	$2$	$5.765$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			722.2.a.h	$2$	$0$	\(-2\)	\(2\)	\(5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{2}+2\beta _{1}q^{3}+\beta _{3}q^{4}+\cdots\)
722.2.c.i	$722$	$2$	722.c	19.c	$3$	$4$	$2$	$5.765$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			722.2.a.h	$2$	$0$	\(2\)	\(-2\)	\(5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{2}-2\beta _{1}q^{3}+\beta _{3}q^{4}+(3+\cdots)q^{5}+\cdots\)
722.2.c.j	$722$	$2$	722.c	19.c	$3$	$4$	$2$	$5.765$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None					38.2.c.b	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
722.2.c.k	$722$	$2$	722.c	19.c	$3$	$6$	$3$	$5.765$	\(\Q(\zeta_{18})\)	None					38.2.e.a	$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(12\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_1-1)q^{2}+(-\beta_{3}+\beta_{2})q^{3}+\cdots\)
722.2.c.l	$722$	$2$	722.c	19.c	$3$	$6$	$3$	$5.765$	\(\Q(\zeta_{18})\)	None					38.2.e.a	$2$	$0$	\(3\)	\(0\)	\(-6\)	\(12\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta_1 q^{2}+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{3}+\cdots\)
722.2.c.m	$722$	$2$	722.c	19.c	$3$	$8$	$4$	$5.765$	8.0.324000000.2	None		✓			722.2.a.m	$2$	$0$	\(-4\)	\(-2\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{4})q^{2}+(\beta _{3}+\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots\)
722.2.c.n	$722$	$2$	722.c	19.c	$3$	$8$	$4$	$5.765$	8.0.324000000.2	None		✓			722.2.a.m	$2$	$0$	\(4\)	\(2\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{4})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(722, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(722, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 2}\)