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

• Label: 450.2.c
• Level: $450$
• Weight: $2$
• Character orbit: 450.c
• Rep. character: $\chi_{450}(199,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	114	8	106
Cusp forms	66	8	58
Eisenstein series	48	0	48

Trace form

8 * q - 8 * q^4 + 6 * q^11 + 4 * q^14 + 8 * q^16 + 14 * q^19 - 4 * q^26 - 12 * q^29 + 4 * q^31 - 18 * q^34 + 18 * q^41 - 6 * q^44 - 12 * q^46 - 4 * q^56 - 8 * q^61 - 8 * q^64 - 24 * q^71 - 8 * q^74 - 14 * q^76 + 20 * q^79 - 16 * q^86 + 66 * q^89 - 64 * q^91 + 24 * q^94

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
450.2.c.a	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	\(\Q(\sqrt{-1}) \)	None					90.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+2 i q^{7}-i q^{8}-6 q^{11}+\cdots\)
450.2.c.b	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	\(\Q(\sqrt{-1}) \)	None					30.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-4 i q^{7}-i q^{8}-2 i q^{13}+\cdots\)
450.2.c.c	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	\(\Q(\sqrt{-1}) \)	None					50.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+2 i q^{7}-i q^{8}+3 q^{11}+\cdots\)
450.2.c.d	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	\(\Q(\sqrt{-1}) \)	None					90.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-2 i q^{7}-i q^{8}+6 q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)