Space of modular forms of level 450, weight 6, and Character 450.c

• Label: 450.6.c
• Level: $450$
• Weight: $6$
• Character orbit: 450.c
• Rep. character: $\chi_{450}(199,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $17$
• Sturm bound: $540$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	450.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(540\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(450, [\chi])\).

	Total	New	Old
Modular forms	474	38	436
Cusp forms	426	38	388
Eisenstein series	48	0	48

Trace form

\( 38 q - 608 q^{4} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(450, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
450.6.c.a	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4iq^{2}-2^{4}q^{4}+142iq^{7}+2^{6}iq^{8}+\cdots\)
450.6.c.b	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2^{4}q^{4}+82iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.c	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-2^{4}q^{4}+74iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.d	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-2^{4}q^{4}+7^{2}iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.e	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4iq^{2}-2^{4}q^{4}+47iq^{7}+2^{6}iq^{8}+\cdots\)
450.6.c.f	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2^{4}q^{4}+59iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.g	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{2}-2^{4}q^{4}+79iq^{7}-2^{6}iq^{8}+\cdots\)
450.6.c.h	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-2^{4}q^{4}+86iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.i	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-2^{4}q^{4}+2^{4}iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.j	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-2^{4}q^{4}+88iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.k	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4iq^{2}-2^{4}q^{4}+iq^{7}+2^{6}iq^{8}+\cdots\)
450.6.c.l	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2^{4}q^{4}+7^{2}iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.m	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2^{4}q^{4}+74iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.n	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{2}-2^{4}q^{4}+233iq^{7}-2^{6}iq^{8}+\cdots\)
450.6.c.o	$450$	$6$	450.c	5.b	$2$	$2$	$2$	$72.173$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-2^{4}q^{4}+11iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.p	$450$	$6$	450.c	5.b	$2$	$4$	$4$	$72.173$	\(\Q(i, \sqrt{4081})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-4\beta _{1}q^{2}-2^{4}q^{4}+(-50\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
450.6.c.q	$450$	$6$	450.c	5.b	$2$	$4$	$4$	$72.173$	\(\Q(i, \sqrt{4081})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4\beta _{1}q^{2}-2^{4}q^{4}+(-50\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)