Space of modular forms of level 420, weight 2, and Character 420.k

• Label: 420.2.k
• Level: $420$
• Weight: $2$
• Character orbit: 420.k
• Rep. character: $\chi_{420}(169,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(420, [\chi])\).

	Total	New	Old
Modular forms	108	4	104
Cusp forms	84	4	80
Eisenstein series	24	0	24

Trace form

4 * q - 4 * q^9 + 4 * q^15 - 8 * q^19 - 4 * q^21 + 12 * q^25 - 24 * q^29 + 8 * q^31 + 4 * q^35 - 8 * q^39 + 16 * q^41 - 4 * q^49 - 8 * q^51 + 32 * q^55 - 16 * q^59 + 24 * q^61 + 8 * q^65 - 8 * q^69 - 16 * q^71 - 32 * q^79 + 4 * q^81 + 8 * q^85 - 48 * q^89 - 8 * q^91 + 32 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(420, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
420.2.k.a	$420$	$2$	420.k	5.b	$2$	$2$	$2$	$3.354$	\(\Q(\sqrt{-1}) \)	None		✓			420.2.k.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i-2)q^{5}+i q^{7}-q^{9}+\cdots\)
420.2.k.b	$420$	$2$	420.k	5.b	$2$	$2$	$2$	$3.354$	\(\Q(\sqrt{-1}) \)	None		✓			420.2.k.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i+2)q^{5}+i q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(420, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)