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

• Label: 900.2.j
• Level: $900$
• Weight: $2$
• Character orbit: 900.j
• Rep. character: $\chi_{900}(557,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• 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.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
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	432	12	420
Cusp forms	288	12	276
Eisenstein series	144	0	144

Trace form

\( 12 q - 8 q^{7} - 12 q^{13} + 24 q^{31} + 12 q^{37} + 40 q^{61} - 32 q^{67} - 28 q^{73} + 24 q^{91} - 12 q^{97}+O(q^{100}) \)

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.j.a	$900$	$2$	900.j	15.e	$4$	$4$	$2$	$7.187$	\(\Q(\zeta_{8})\)	None					180.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\beta_1-2)q^{7}+2\beta_{2} q^{11}+(-3\beta_1-3)q^{13}+\cdots\)
900.2.j.b	$900$	$2$	900.j	15.e	$4$	$8$	$4$	$7.187$	\(\Q(\zeta_{24})\)	None		✓	✓		900.2.j.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_{3} q^{7}-\beta_{5} q^{11}-\beta_1 q^{13}+\beta_{6} q^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)