Space of modular forms of level 825, weight 2, and Character 825.j

• Label: 825.2.j
• Level: $825$
• Weight: $2$
• Character orbit: 825.j
• Rep. character: $\chi_{825}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).

	Total	New	Old
Modular forms	264	72	192
Cusp forms	216	72	144
Eisenstein series	48	0	48

Trace form

72 * q + 16 * q^11 - 16 * q^12 - 104 * q^16 - 32 * q^22 + 32 * q^23 + 32 * q^31 - 16 * q^33 - 72 * q^36 + 8 * q^37 + 56 * q^38 - 8 * q^42 - 32 * q^48 - 24 * q^53 - 80 * q^56 + 24 * q^58 + 32 * q^66 + 32 * q^67 + 64 * q^71 - 24 * q^77 + 24 * q^78 - 72 * q^81 + 72 * q^82 + 80 * q^86 - 104 * q^88 + 32 * q^91 - 80 * q^92 + 48 * q^93 - 88 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
825.2.j.a	$825$	$2$	825.j	55.e	$4$	$8$	$4$	$6.588$	\(\Q(\zeta_{24})\)	None		✓			825.2.j.a	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_{2} q^{2}-\beta_1 q^{3}+(-\beta_{6}+\beta_{2}-1)q^{4}+\cdots\)
825.2.j.b	$825$	$2$	825.j	55.e	$4$	$8$	$4$	$6.588$	\(\Q(\zeta_{24})\)	None		✓			825.2.j.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{3}-\beta_{2}+1)q^{2}-\beta_1 q^{3}+(\beta_{6}-\beta_{2}+1)q^{4}+\cdots\)
825.2.j.c	$825$	$2$	825.j	55.e	$4$	$24$	$12$	$6.588$		None					165.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
825.2.j.d	$825$	$2$	825.j	55.e	$4$	$32$	$16$	$6.588$		None		✓	✓		825.2.j.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(825, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)