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

• Label: 900.2.be
• Level: $900$
• Weight: $2$
• Character orbit: 900.be
• Rep. character: $\chi_{900}(257,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $360$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(360\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	792	72	720
Cusp forms	648	72	576
Eisenstein series	144	0	144

Trace form

72 * q + 2 * q^3 - 24 * q^11 - 8 * q^21 + 24 * q^23 + 26 * q^27 + 26 * q^33 - 12 * q^37 + 72 * q^41 + 42 * q^47 + 32 * q^51 + 14 * q^57 + 24 * q^61 - 34 * q^63 - 6 * q^67 - 96 * q^77 - 52 * q^81 - 60 * q^83 - 88 * q^87 + 48 * q^91 - 52 * q^93 + 18 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
900.2.be.a	$900$	$2$	900.be	45.l	$12$	$4$	$1$	$7.187$	\(\Q(\zeta_{12})\)	None		✓			900.2.be.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2+\zeta_{12}^{2})q^{3}+(2+2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
900.2.be.b	$900$	$2$	900.be	45.l	$12$	$4$	$1$	$7.187$	\(\Q(\zeta_{12})\)	None		✓			900.2.be.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}+\cdots)q^{7}+\cdots\)
900.2.be.c	$900$	$2$	900.be	45.l	$12$	$4$	$1$	$7.187$	\(\Q(\zeta_{12})\)	None		✓			900.2.be.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(1+\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
900.2.be.d	$900$	$2$	900.be	45.l	$12$	$4$	$1$	$7.187$	\(\Q(\zeta_{12})\)	None		✓			900.2.be.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2-\zeta_{12}^{2})q^{3}+(-2-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
900.2.be.e	$900$	$2$	900.be	45.l	$12$	$24$	$6$	$7.187$		None					180.2.w.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
900.2.be.f	$900$	$2$	900.be	45.l	$12$	$32$	$8$	$7.187$		None		✓	✓		900.2.be.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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