Space of modular forms of level 675, weight 2, and Character 675.h

• Label: 675.2.h
• Level: $675$
• Weight: $2$
• Character orbit: 675.h
• Rep. character: $\chi_{675}(136,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $160$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.h (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

	Total	New	Old
Modular forms	384	160	224
Cusp forms	336	160	176
Eisenstein series	48	0	48

Trace form

\( 160 q - 40 q^{4} + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
675.2.h.a	$675$	$2$	675.h	25.d	$5$	$40$	$10$	$5.390$		None		$2$	$0$	\(-2\)	\(0\)	\(-3\)	\(-2\)		$\mathrm{SU}(2)[C_{5}]$
675.2.h.b	$675$	$2$	675.h	25.d	$5$	$40$	$10$	$5.390$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(20\)		$\mathrm{SU}(2)[C_{5}]$
675.2.h.c	$675$	$2$	675.h	25.d	$5$	$40$	$10$	$5.390$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{5}]$
675.2.h.d	$675$	$2$	675.h	25.d	$5$	$40$	$10$	$5.390$		None		$2$	$0$	\(2\)	\(0\)	\(3\)	\(-2\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)