Space of modular forms of level 900, weight 2, and Character 900.r

• Label: 900.2.r
• Level: $900$
• Weight: $2$
• Character orbit: 900.r
• Rep. character: $\chi_{900}(551,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Newform subspaces: $7$
• Sturm bound: $360$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(360\)
Trace bound:			\(12\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).

	Total	New	Old
Modular forms	384	240	144
Cusp forms	336	216	120
Eisenstein series	48	24	24

Trace form

\( 216 q + 3 q^{2} + q^{4} - 11 q^{6} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
900.2.r.a	$900$	$2$	900.r	36.h	$6$	$8$	$4$	$7.187$	8.0.3317760000.3	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{3}-\beta _{5})q^{3}-2\beta _{4}q^{4}+\cdots\)
900.2.r.b	$900$	$2$	900.r	36.h	$6$	$8$	$4$	$7.187$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{3}q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4})q^{3}+\cdots\)
900.2.r.c	$900$	$2$	900.r	36.h	$6$	$8$	$4$	$7.187$	8.0.170772624.1	None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3}-\beta _{4}-\beta _{7})q^{3}+\cdots\)
900.2.r.d	$900$	$2$	900.r	36.h	$6$	$48$	$24$	$7.187$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
900.2.r.e	$900$	$2$	900.r	36.h	$6$	$48$	$24$	$7.187$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
900.2.r.f	$900$	$2$	900.r	36.h	$6$	$48$	$24$	$7.187$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
900.2.r.g	$900$	$2$	900.r	36.h	$6$	$48$	$24$	$7.187$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)