Space of modular forms of level 700, weight 2, and Character 700.r

• Label: 700.2.r
• Level: $700$
• Weight: $2$
• Character orbit: 700.r
• Rep. character: $\chi_{700}(149,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).

	Total	New	Old
Modular forms	276	24	252
Cusp forms	204	24	180
Eisenstein series	72	0	72

Trace form

24 * q + 20 * q^9 - 10 * q^11 + 10 * q^19 + 4 * q^21 + 12 * q^31 + 16 * q^39 + 76 * q^41 - 24 * q^49 + 24 * q^51 - 8 * q^59 - 44 * q^61 - 36 * q^69 - 44 * q^71 - 28 * q^79 - 68 * q^81 + 22 * q^89 + 26 * q^91 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(700, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
700.2.r.a	$700$	$2$	700.r	35.j	$6$	$4$	$2$	$5.590$	\(\Q(\zeta_{12})\)	None					140.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
700.2.r.b	$700$	$2$	700.r	35.j	$6$	$4$	$2$	$5.590$	\(\Q(\zeta_{12})\)	None					28.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
700.2.r.c	$700$	$2$	700.r	35.j	$6$	$4$	$2$	$5.590$	\(\Q(\zeta_{12})\)	None					140.2.i.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}q^{3}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+6\zeta_{12}^{2}q^{9}+\cdots\)
700.2.r.d	$700$	$2$	700.r	35.j	$6$	$12$	$6$	$5.590$	12.0.\(\cdots\).1	None		✓	✓		700.2.i.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{4}-\beta _{10})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces

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