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

• Label: 900.2.n
• Level: $900$
• Weight: $2$
• Character orbit: 900.n
• Rep. character: $\chi_{900}(181,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $52$
• Newform subspaces: $4$
• 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.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(360\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	768	52	716
Cusp forms	672	52	620
Eisenstein series	96	0	96

Trace form

52 * q + 4 * q^5 + 6 * q^7 - q^11 - 6 * q^13 - 11 * q^17 + 4 * q^19 + 6 * q^23 + 4 * q^25 - 6 * q^29 - 7 * q^35 + 23 * q^37 - 7 * q^41 + 34 * q^43 + 39 * q^47 + 74 * q^49 + 9 * q^53 + 5 * q^55 + 27 * q^59 + 2 * q^61 + 28 * q^65 + 35 * q^67 + 19 * q^71 - 2 * q^73 + 20 * q^77 + 8 * q^79 + 36 * q^83 + 34 * q^85 + 32 * q^89 + 36 * q^91 + 14 * q^95 - 55 * 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.n.a	$900$	$2$	900.n	25.d	$5$	$8$	$2$	$7.187$	\(\Q(\zeta_{15})\)	None					300.2.m.a	$2$	$0$	\(0\)	\(0\)	\(-5\)	\(-8\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta_{7}+\beta_{6}+\beta_{5}+\cdots+1)q^{5}+\cdots\)
900.2.n.b	$900$	$2$	900.n	25.d	$5$	$8$	$2$	$7.187$	8.0.26265625.1	None					300.2.m.b	$2$	$0$	\(0\)	\(0\)	\(5\)	\(8\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(1+\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\)
900.2.n.c	$900$	$2$	900.n	25.d	$5$	$12$	$3$	$7.187$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					100.2.g.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\beta _{4}-\beta _{5}+\beta _{6}+\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
900.2.n.d	$900$	$2$	900.n	25.d	$5$	$24$	$6$	$7.187$		None		✓	✓		900.2.n.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)