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

• Label: 900.2.w
• Level: $900$
• Weight: $2$
• Character orbit: 900.w
• Rep. character: $\chi_{900}(109,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $48$
• Newform subspaces: $3$
• 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.w (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
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	768	48	720
Cusp forms	672	48	624
Eisenstein series	96	0	96

Trace form

48 * q - 3 * q^5 + q^11 - 5 * q^17 + 4 * q^19 - 20 * q^23 - 19 * q^25 + 4 * q^29 + 11 * q^35 - 3 * q^41 - 5 * q^47 - 26 * q^49 + 30 * q^53 + 43 * q^55 + 27 * q^59 - 12 * q^61 + 25 * q^65 + 35 * q^67 - 39 * q^71 + 60 * q^73 + 60 * q^77 + 8 * q^79 + 60 * q^83 - 11 * q^85 + 37 * q^89 - 36 * q^91 + 30 * q^95 + 5 * 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.w.a	$900$	$2$	900.w	25.e	$10$	$8$	$2$	$7.187$	8.0.58140625.2	None					100.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-2\beta _{1}-\beta _{2}-\beta _{5}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
900.2.w.b	$900$	$2$	900.w	25.e	$10$	$16$	$4$	$7.187$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			900.2.w.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{12}q^{5}+(-\beta _{3}-\beta _{4}+\beta _{9})q^{7}+(-\beta _{11}+\cdots)q^{11}+\cdots\)
900.2.w.c	$900$	$2$	900.w	25.e	$10$	$24$	$6$	$7.187$		None			✓		300.2.o.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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