Space of modular forms of level 700, weight 5, and Character 700.o

• Label: 700.5.o
• Level: $700$
• Weight: $5$
• Character orbit: 700.o
• Rep. character: $\chi_{700}(549,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $600$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(600\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(700, [\chi])\).

	Total	New	Old
Modular forms	996	96	900
Cusp forms	924	96	828
Eisenstein series	72	0	72

Trace form

96 * q - 1332 * q^9 - 330 * q^11 + 78 * q^19 - 1004 * q^21 + 1176 * q^29 - 2652 * q^31 - 588 * q^39 + 3616 * q^49 - 1420 * q^51 - 4716 * q^59 - 11100 * q^61 - 22308 * q^71 - 8008 * q^79 - 24536 * q^81 - 35622 * q^89 - 20974 * q^91 + 145860 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(700, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
700.5.o.a	$700$	$5$	700.o	35.i	$6$	$12$	$6$	$72.359$	12.0.\(\cdots\).37	None					28.5.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2\beta _{1}+\beta _{2}+\beta _{8})q^{3}+(-9\beta _{1}+4\beta _{2}+\cdots)q^{7}+\cdots\)
700.5.o.b	$700$	$5$	700.o	35.i	$6$	$40$	$20$	$72.359$		None					140.5.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
700.5.o.c	$700$	$5$	700.o	35.i	$6$	$44$	$22$	$72.359$		None		✓	✓		700.5.s.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{5}^{\mathrm{old}}(700, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(700, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)