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

• Label: 700.2.e
• Level: $700$
• Weight: $2$
• Character orbit: 700.e
• Rep. character: $\chi_{700}(449,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	138	8	130
Cusp forms	102	8	94
Eisenstein series	36	0	36

Trace form

8 * q - 4 * q^9 - 8 * q^11 - 8 * q^19 - 8 * q^21 + 24 * q^29 + 28 * q^31 + 4 * q^39 - 28 * q^41 - 8 * q^49 - 12 * q^51 + 20 * q^59 - 12 * q^61 - 36 * q^69 + 20 * q^71 - 24 * q^79 + 16 * q^81 - 28 * q^89 - 16 * q^91 + 36 * 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.e.a	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	\(\Q(\sqrt{-1}) \)	None					140.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+i q^{7}-6 q^{9}-5 q^{11}+\cdots\)
700.2.e.b	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	\(\Q(\sqrt{-1}) \)	None		✓			700.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+i q^{7}-q^{9}+3 q^{11}+4 i q^{13}+\cdots\)
700.2.e.c	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	\(\Q(\sqrt{-1}) \)	None					140.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{7}+2 q^{9}+3 q^{11}-i q^{13}+\cdots\)
700.2.e.d	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	\(\Q(\sqrt{-1}) \)	None		✓			700.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{7}+3 q^{9}-5 q^{11}-6 i q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)