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

• Label: 900.2.bj
• Level: $900$
• Weight: $2$
• Character orbit: 900.bj
• Rep. character: $\chi_{900}(127,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $584$
• Newform subspaces: $6$
• Sturm bound: $360$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(360\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	1504	616	888
Cusp forms	1376	584	792
Eisenstein series	128	32	96

Trace form

584 * q + 8 * q^2 - 10 * q^4 + 16 * q^5 + 2 * q^8 - 18 * q^13 + 10 * q^14 - 6 * q^16 + 6 * q^17 + 26 * q^20 + 6 * q^22 - 26 * q^25 + 16 * q^26 + 22 * q^28 + 20 * q^29 + 38 * q^32 - 10 * q^34 - 14 * q^37 + 56 * q^38 + 20 * q^40 + 12 * q^41 + 80 * q^44 - 6 * q^46 + 70 * q^50 + 28 * q^52 + 42 * q^53 + 6 * q^56 + 36 * q^58 - 12 * q^61 + 4 * q^62 + 20 * q^64 + 42 * q^65 - 18 * q^68 - 26 * q^70 + 18 * q^73 + 68 * q^77 + 30 * q^80 + 62 * q^82 + 16 * q^85 + 6 * q^86 + 78 * q^88 + 150 * q^89 - 34 * q^92 - 90 * q^94 - 166 * q^97 - 112 * q^98

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.bj.a	$900$	$2$	900.bj	100.l	$20$	$8$	$1$	$7.187$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)					100.2.l.a	$4$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
900.2.bj.b	$900$	$2$	900.bj	100.l	$20$	$8$	$1$	$7.187$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		✓			900.2.bj.b	$4$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
900.2.bj.c	$900$	$2$	900.bj	100.l	$20$	$8$	$1$	$7.187$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		✓			900.2.bj.b	$4$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
900.2.bj.d	$900$	$2$	900.bj	100.l	$20$	$96$	$12$	$7.187$		None					100.2.l.b	$4$	$0$	\(10\)	\(0\)	\(20\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
900.2.bj.e	$900$	$2$	900.bj	100.l	$20$	$224$	$28$	$7.187$		None		✓			900.2.bj.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
900.2.bj.f	$900$	$2$	900.bj	100.l	$20$	$240$	$30$	$7.187$		None			✓		300.2.w.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

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

\( S_{2}^{\mathrm{old}}(900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)