Space of modular forms of level 900, weight 6, and Character 900.j

• Label: 900.6.j
• Level: $900$
• Weight: $6$
• Character orbit: 900.j
• Rep. character: $\chi_{900}(557,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $1080$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	900.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(1080\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

	Total	New	Old
Modular forms	1872	60	1812
Cusp forms	1728	60	1668
Eisenstein series	144	0	144

Trace form

\( 60 q + 152 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
900.6.j.a	$900$	$6$	900.j	15.e	$4$	$16$	$8$	$144.345$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 3^{24}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{7}+(-\beta _{11}+\beta _{14})q^{11}+(\beta _{6}+\cdots)q^{13}+\cdots\)
900.6.j.b	$900$	$6$	900.j	15.e	$4$	$20$	$10$	$144.345$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(152\)	$2^{46}\cdot 3^{24}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(8-8\beta _{3}-\beta _{7})q^{7}+\beta _{18}q^{11}+(-13+\cdots)q^{13}+\cdots\)
900.6.j.c	$900$	$6$	900.j	15.e	$4$	$24$	$12$	$144.345$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{6}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)