Space of modular forms of level 210, weight 2, and Character 210.g

• Label: 210.2.g
• Level: $210$
• Weight: $2$
• Character orbit: 210.g
• Rep. character: $\chi_{210}(169,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).

	Total	New	Old
Modular forms	56	4	52
Cusp forms	40	4	36
Eisenstein series	16	0	16

Trace form

4 * q - 4 * q^4 - 4 * q^9 - 8 * q^15 + 4 * q^16 + 16 * q^19 - 4 * q^21 - 12 * q^25 + 16 * q^26 + 4 * q^30 + 8 * q^31 - 24 * q^34 - 8 * q^35 + 4 * q^36 - 8 * q^39 + 16 * q^41 - 16 * q^46 - 4 * q^49 + 16 * q^50 - 8 * q^51 + 8 * q^55 + 32 * q^59 + 8 * q^60 - 4 * q^64 - 16 * q^65 + 8 * q^66 + 16 * q^69 + 4 * q^70 - 40 * q^71 - 24 * q^74 - 16 * q^76 + 16 * q^79 + 4 * q^81 + 4 * q^84 - 16 * q^85 + 24 * q^86 - 8 * q^91 - 24 * q^94 + 8 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
210.2.g.a	$210$	$2$	210.g	5.b	$2$	$2$	$2$	$1.677$	\(\Q(\sqrt{-1}) \)	None		✓			210.2.g.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}+(2 i-1)q^{5}+\cdots\)
210.2.g.b	$210$	$2$	210.g	5.b	$2$	$2$	$2$	$1.677$	\(\Q(\sqrt{-1}) \)	None		✓			210.2.g.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(210, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)