Space of modular forms of level 825, weight 3, and Character 825.b

• Label: 825.3.b
• Level: $825$
• Weight: $3$
• Character orbit: 825.b
• Rep. character: $\chi_{825}(76,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $5$
• Sturm bound: $360$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	825.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(360\)
Trace bound:			\(22\)
Distinguishing \(T_p\):			\(2\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(825, [\chi])\).

	Total	New	Old
Modular forms	252	76	176
Cusp forms	228	76	152
Eisenstein series	24	0	24

Trace form

\( 76 q - 164 q^{4} + 228 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
825.3.b.a	$825$	$3$	825.b	11.b	$2$	$4$	$4$	$22.480$	4.0.39744.5	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(-5-2\beta _{1})q^{4}+\cdots\)
825.3.b.b	$825$	$3$	825.b	11.b	$2$	$16$	$16$	$22.480$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-3+\beta _{2})q^{4}-\beta _{7}q^{6}+\cdots\)
825.3.b.c	$825$	$3$	825.b	11.b	$2$	$16$	$16$	$22.480$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots\)
825.3.b.d	$825$	$3$	825.b	11.b	$2$	$16$	$16$	$22.480$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-\beta _{5}q^{6}+\cdots\)
825.3.b.e	$825$	$3$	825.b	11.b	$2$	$24$	$24$	$22.480$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)