Space of modular forms of level 450, weight 2, and Character 450.j

• Label: 450.2.j
• Level: $450$
• Weight: $2$
• Character orbit: 450.j
• Rep. character: $\chi_{450}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $7$
• Sturm bound: $180$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(180\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(450, [\chi])\).

	Total	New	Old
Modular forms	204	36	168
Cusp forms	156	36	120
Eisenstein series	48	0	48

Trace form

\( 36 q + 18 q^{4} - 8 q^{6} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
450.2.j.a	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.b	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.c	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.d	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.e	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.f	$450$	$2$	450.j	45.j	$6$	$8$	$4$	$3.593$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)
450.2.j.g	$450$	$2$	450.j	45.j	$6$	$8$	$4$	$3.593$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3}-\beta _{5}-\beta _{7})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)