Space of modular forms of level 300, weight 3, and Character 300.q

• Label: 300.3.q
• Level: $300$
• Weight: $3$
• Character orbit: 300.q
• Rep. character: $\chi_{300}(29,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.q (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(300, [\chi])\).

	Total	New	Old
Modular forms	504	80	424
Cusp forms	456	80	376
Eisenstein series	48	0	48

Trace form

\( 80 q - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(300, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.3.q.a	$300$	$3$	300.q	75.h	$10$	$80$	$20$	$8.174$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)