Space of modular forms of level 375, weight 3, and Character 375.j

• Label: 375.3.j
• Level: $375$
• Weight: $3$
• Character orbit: 375.j
• Rep. character: $\chi_{375}(26,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $216$
• Newform subspaces: $2$
• Sturm bound: $150$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(150\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(375, [\chi])\).

	Total	New	Old
Modular forms	440	264	176
Cusp forms	360	216	144
Eisenstein series	80	48	32

Trace form

\( 216 q + q^{3} + 102 q^{4} - q^{6} + 8 q^{7} + 13 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(375, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
375.3.j.a	$375$	$3$	375.j	75.j	$10$	$72$	$18$	$10.218$		None					75.3.j.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{10}]$
375.3.j.b	$375$	$3$	375.j	75.j	$10$	$144$	$36$	$10.218$		None			✓		75.3.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(375, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(375, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)