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

• Label: 900.2.z
• Level: $900$
• Weight: $2$
• Character orbit: 900.z
• Rep. character: $\chi_{900}(179,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $240$
• Newform subspaces: $2$
• Sturm bound: $360$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.z (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 300 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(360\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	752	240	512
Cusp forms	688	240	448
Eisenstein series	64	0	64

Trace form

\( 240 q - 8 q^{10} - 24 q^{16} + 8 q^{25} + 32 q^{34} + 20 q^{37} + 44 q^{40} - 40 q^{46} + 256 q^{49} - 100 q^{52} - 120 q^{58} + 8 q^{61} - 48 q^{64} - 40 q^{70} + 24 q^{76} - 120 q^{88} - 4 q^{94} + 200 q^{97}+O(q^{100}) \)

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.z.a	$900$	$2$	900.z	300.r	$10$	$16$	$4$	$7.187$	\(\Q(\zeta_{40})\)	\(\Q(\sqrt{-1}) \)		✓			900.2.z.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{8}$	$\mathrm{U}(1)[D_{10}]$	\(q+\beta_{11} q^{2}-2\beta_{7} q^{4}+(-\beta_{12}+\beta_{8})q^{5}+\cdots\)
900.2.z.b	$900$	$2$	900.z	300.r	$10$	$224$	$56$	$7.187$		None		✓	✓		900.2.z.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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