Space of modular forms of level 300, weight 1, and Character 300.g

• Label: 300.1.g
• Level: $300$
• Weight: $1$
• Character orbit: 300.g
• Rep. character: $\chi_{300}(101,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	300.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(300, [\chi])\).

	Total	New	Old
Modular forms	20	2	18
Cusp forms	2	2	0
Eisenstein series	18	0	18

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(300, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.1.g.a	$300$	$1$	300.g	3.b	$2$	$1$	$1$	$0.150$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{3}+q^{7}+q^{9}+q^{13}-q^{19}-q^{21}+\cdots\)
300.1.g.b	$300$	$1$	300.g	3.b	$2$	$1$	$1$	$0.150$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{3}-q^{7}+q^{9}-q^{13}-q^{19}-q^{21}+\cdots\)