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

• Label: 900.2.bn
• Level: $900$
• Weight: $2$
• Character orbit: 900.bn
• Rep. character: $\chi_{900}(59,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $1408$
• Newform subspaces: $1$
• Sturm bound: $360$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bn (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 900 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(360\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	1472	1472	0
Cusp forms	1408	1408	0
Eisenstein series	64	64	0

Trace form

1408 * q - 15 * q^2 - 3 * q^4 - 24 * q^5 - 2 * q^6 - 12 * q^9 - 20 * q^10 - 10 * q^12 - 10 * q^13 - 9 * q^14 - 3 * q^16 + 9 * q^20 + 6 * q^21 - 5 * q^22 - 14 * q^24 - 8 * q^25 + 20 * q^28 - 18 * q^29 + 22 * q^30 - 20 * q^33 + q^34 + 16 * q^36 - 40 * q^37 - 15 * q^38 + q^40 - 18 * q^41 - 80 * q^42 + 6 * q^45 - 4 * q^46 + 55 * q^48 - 624 * q^49 + 27 * q^50 - 5 * q^52 + 37 * q^54 + 54 * q^56 - 5 * q^58 - 103 * q^60 - 6 * q^61 - 12 * q^64 + 62 * q^66 + 24 * q^69 - 24 * q^70 - 10 * q^72 - 40 * q^73 - 78 * q^74 - 16 * q^76 - 30 * q^77 - 170 * q^78 + 36 * q^81 - 57 * q^84 + 2 * q^85 - 69 * q^86 - 5 * q^88 - 3 * q^90 - 15 * q^92 - 31 * q^94 - 53 * q^96 - 10 * 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.bn.a	$900$	$2$	900.bn	900.an	$30$	$1408$	$176$	$7.187$		None		✓	✓	✓	900.2.bn.a	$8$	$0$	\(-15\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$