Space of modular forms of level 900, weight 3, and Character 900.g

• Label: 900.3.g
• Level: $900$
• Weight: $3$
• Character orbit: 900.g
• Rep. character: $\chi_{900}(701,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $540$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(540\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

	Total	New	Old
Modular forms	396	12	384
Cusp forms	324	12	312
Eisenstein series	72	0	72

Trace form

\( 12 q + 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
900.3.g.a	$900$	$3$	900.g	3.b	$2$	$2$	$2$	$24.523$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{7}+\beta q^{11}-7q^{13}-\beta q^{17}-7q^{19}+\cdots\)
900.3.g.b	$900$	$3$	900.g	3.b	$2$	$2$	$2$	$24.523$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{7}+\beta q^{11}+7q^{13}+\beta q^{17}-7q^{19}+\cdots\)
900.3.g.c	$900$	$3$	900.g	3.b	$2$	$4$	$4$	$24.523$	\(\Q(\sqrt{-2}, \sqrt{-23})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{7}-7\beta _{1}q^{11}+3\beta _{2}q^{13}-2\beta _{3}q^{17}+\cdots\)
900.3.g.d	$900$	$3$	900.g	3.b	$2$	$4$	$4$	$24.523$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(4-\beta _{2})q^{7}+(-\beta _{1}+\beta _{3})q^{11}+(-2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)