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

• Label: 900.2.bq
• Level: $900$
• Weight: $2$
• Character orbit: 900.bq
• Rep. character: $\chi_{900}(169,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $240$
• 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.bq (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
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	1488	240	1248
Cusp forms	1392	240	1152
Eisenstein series	96	0	96

Trace form

240 * q + 4 * q^5 - 2 * q^9 - 4 * q^11 - 35 * q^15 - 12 * q^21 - 12 * q^25 - 15 * q^27 + 12 * q^29 - 6 * q^31 - 25 * q^33 + 34 * q^35 + 8 * q^39 - 16 * q^41 - 69 * q^45 + 25 * q^47 + 120 * q^49 - 2 * q^51 + 6 * q^55 + 9 * q^59 + 5 * q^63 + 35 * q^65 + 15 * q^67 + 10 * q^69 - 38 * q^71 - 36 * q^75 - 40 * q^77 + 12 * q^79 - 18 * q^81 + 70 * q^83 + 12 * q^85 - 75 * q^87 - 58 * q^89 - 36 * q^95 - 46 * q^99

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.bq.a	$900$	$2$	900.bq	225.u	$30$	$240$	$30$	$7.187$		None		✓	✓	✓	900.2.bq.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$

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

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