Space of modular forms of level 714, weight 2, and Character 714.i

• Label: 714.2.i
• Level: $714$
• Weight: $2$
• Character orbit: 714.i
• Rep. character: $\chi_{714}(205,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $15$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(714, [\chi])\).

	Total	New	Old
Modular forms	304	40	264
Cusp forms	272	40	232
Eisenstein series	32	0	32

Trace form

40 * q - 20 * q^4 + 8 * q^6 - 4 * q^7 - 20 * q^9 - 4 * q^10 + 8 * q^11 - 8 * q^14 - 8 * q^15 - 20 * q^16 + 16 * q^19 - 8 * q^21 - 8 * q^22 - 16 * q^23 - 4 * q^24 - 24 * q^25 + 8 * q^26 - 4 * q^28 + 32 * q^29 - 12 * q^31 + 4 * q^33 + 16 * q^34 + 32 * q^35 + 40 * q^36 + 8 * q^37 + 8 * q^38 - 8 * q^39 - 4 * q^40 - 64 * q^41 - 4 * q^42 + 48 * q^43 + 8 * q^44 + 8 * q^46 - 40 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^53 - 4 * q^54 - 40 * q^55 + 16 * q^56 + 32 * q^57 + 4 * q^58 - 24 * q^59 + 4 * q^60 - 16 * q^61 - 48 * q^62 + 8 * q^63 + 40 * q^64 + 40 * q^65 - 8 * q^67 + 44 * q^70 - 48 * q^71 + 24 * q^74 - 32 * q^76 + 48 * q^77 - 20 * q^79 - 20 * q^81 + 96 * q^83 + 16 * q^84 + 40 * q^86 + 4 * q^87 + 4 * q^88 + 8 * q^89 + 8 * q^90 + 80 * q^91 + 32 * q^92 + 8 * q^94 - 32 * q^95 - 4 * q^96 - 56 * q^97 - 8 * q^98 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(714, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
714.2.i.a	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.a	$2$	$1$	\(-1\)	\(-1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.b	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.b	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.c	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.c	$2$	$0$	\(-1\)	\(1\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.d	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.d	$2$	$1$	\(-1\)	\(1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.e	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.e	$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.f	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.f	$2$	$0$	\(-1\)	\(1\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.g	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.g	$2$	$0$	\(1\)	\(-1\)	\(-3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.h	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.h	$2$	$0$	\(1\)	\(-1\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.i	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.i	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.j	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.j	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.k	$714$	$2$	714.i	7.c	$3$	$2$	$1$	$5.701$	\(\Q(\sqrt{-3}) \)	None		✓			714.2.i.k	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.l	$714$	$2$	714.i	7.c	$3$	$4$	$2$	$5.701$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓			714.2.i.l	$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
714.2.i.m	$714$	$2$	714.i	7.c	$3$	$4$	$2$	$5.701$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓			714.2.i.m	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
714.2.i.n	$714$	$2$	714.i	7.c	$3$	$4$	$2$	$5.701$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			714.2.i.n	$2$	$0$	\(2\)	\(-2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
714.2.i.o	$714$	$2$	714.i	7.c	$3$	$6$	$3$	$5.701$	6.0.11337408.1	None		✓	✓		714.2.i.o	$2$	$0$	\(3\)	\(3\)	\(3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(1-\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(714, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(714, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)