Space of modular forms of level 2420, weight 1, and Character 2420.q

• Label: 2420.1.q
• Level: $2420$
• Weight: $1$
• Character orbit: 2420.q
• Rep. character: $\chi_{2420}(1129,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $396$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2420.q (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(396\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2420, [\chi])\).

	Total	New	Old
Modular forms	164	8	156
Cusp forms	20	8	12
Eisenstein series	144	0	144

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - q^{5} + 4 q^{9} - 3 q^{15} + q^{25} - 2 q^{31} - 8 q^{45} + 2 q^{49} + 2 q^{59} - 6 q^{69} + 2 q^{71} - 3 q^{75} - 2 q^{81} + 8 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2420, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2420.1.q.a	$2420$	$1$	2420.q	55.h	$10$	$8$	$2$	$1.208$	\(\Q(\zeta_{15})\)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None			✓	✓	220.1.e.a	$16$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(\zeta_{30}^{2}+\zeta_{30}^{7})q^{3}+\zeta_{30}^{11}q^{5}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2420, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2420, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 3}\)