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

• Label: 900.3.p
• Level: $900$
• Weight: $3$
• Character orbit: 900.p
• Rep. character: $\chi_{900}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $6$
• Sturm bound: $540$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(540\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	756	76	680
Cusp forms	684	76	608
Eisenstein series	72	0	72

Trace form

\( 76 q + q^{3} - q^{7} + 19 q^{9} + O(q^{10}) \)

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.p.a	$900$	$3$	900.p	9.d	$6$	$4$	$2$	$24.523$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{3})q^{3}+(-\beta _{1}+3\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
900.3.p.b	$900$	$3$	900.p	9.d	$6$	$4$	$2$	$24.523$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-8\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\beta _{1}q^{3}+(-4\beta _{1}-\beta _{2})q^{7}+(-9+\cdots)q^{9}+\cdots\)
900.3.p.c	$900$	$3$	900.p	9.d	$6$	$12$	$6$	$24.523$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6})q^{7}+\cdots\)
900.3.p.d	$900$	$3$	900.p	9.d	$6$	$16$	$8$	$24.523$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(1\)	$3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{4})q^{3}-\beta _{10}q^{7}+(1-\beta _{3}+\beta _{15})q^{9}+\cdots\)
900.3.p.e	$900$	$3$	900.p	9.d	$6$	$16$	$8$	$24.523$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-1\)	$3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{4})q^{3}+\beta _{10}q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
900.3.p.f	$900$	$3$	900.p	9.d	$6$	$24$	$12$	$24.523$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)