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

• Label: 2420.1.h
• Level: $2420$
• Weight: $1$
• Character orbit: 2420.h
• Rep. character: $\chi_{2420}(2179,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $10$
• Sturm bound: $396$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2420.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(396\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	40	34	6
Cusp forms	16	16	0
Eisenstein series	24	18	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 4 q^{4} - 2 q^{5} + O(q^{10}) \)

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.h.a	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	✓			2420.1.h.a	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(1\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2420.1.h.b	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{11}) \)	✓	✓			2420.1.h.b	$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(-2\)	$1$		\(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}-q^{9}+\cdots\)
2420.1.h.c	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	✓			2420.1.h.a	$2$	$0$	\(-1\)	\(1\)	\(1\)	\(1\)	$1$		\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2420.1.h.d	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	✓			2420.1.h.a	$2$	$0$	\(1\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2420.1.h.e	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{11}) \)	✓	✓			2420.1.h.b	$4$	$0$	\(1\)	\(0\)	\(-1\)	\(2\)	$1$		\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{9}+\cdots\)
2420.1.h.f	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	✓			2420.1.h.a	$2$	$0$	\(1\)	\(1\)	\(1\)	\(-1\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2420.1.h.g	$2420$	$1$	2420.h	20.d	$2$	$2$	$2$	$1.208$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None	✓	✓			2420.1.h.g	$4$	$0$	\(-2\)	\(0\)	\(-2\)	\(2\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots\)
2420.1.h.h	$2420$	$1$	2420.h	20.d	$2$	$2$	$2$	$1.208$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{55}) \)		✓			2420.1.h.h	$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-iq^{2}-q^{4}+q^{5}+iq^{8}-q^{9}-iq^{10}+\cdots\)
2420.1.h.i	$2420$	$1$	2420.h	20.d	$2$	$2$	$2$	$1.208$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None	✓	✓			2420.1.h.g	$4$	$0$	\(2\)	\(0\)	\(-2\)	\(-2\)	$1$		\(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{7}+\cdots\)
2420.1.h.j	$2420$	$1$	2420.h	20.d	$2$	$4$	$4$	$1.208$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		✓	✓		2420.1.h.j	$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)