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

• Label: 825.2.c
• Level: $825$
• Weight: $2$
• Character orbit: 825.c
• Rep. character: $\chi_{825}(199,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $7$
• Sturm bound: $240$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(240\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	132	28	104
Cusp forms	108	28	80
Eisenstein series	24	0	24

Trace form

\( 28 q - 32 q^{4} + 8 q^{6} - 28 q^{9} + O(q^{10}) \)

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.c.a	$825$	$2$	825.c	5.b	$2$	$2$	$2$	$6.588$	\(\Q(\sqrt{-1}) \)	None					33.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
825.2.c.b	$825$	$2$	825.c	5.b	$2$	$2$	$2$	$6.588$	\(\Q(\sqrt{-1}) \)	None		✓			825.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-q^{11}+\cdots\)
825.2.c.c	$825$	$2$	825.c	5.b	$2$	$4$	$4$	$6.588$	\(\Q(\zeta_{12})\)	None					165.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{3}q^{6}+\cdots\)
825.2.c.d	$825$	$2$	825.c	5.b	$2$	$4$	$4$	$6.588$	\(\Q(\zeta_{8})\)	None		✓			825.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.e	$825$	$2$	825.c	5.b	$2$	$4$	$4$	$6.588$	\(\Q(\zeta_{8})\)	None					165.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.f	$825$	$2$	825.c	5.b	$2$	$6$	$6$	$6.588$	6.0.5161984.1	None		✓			825.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-3-\beta _{1}+\cdots)q^{4}+\cdots\)
825.2.c.g	$825$	$2$	825.c	5.b	$2$	$6$	$6$	$6.588$	6.0.350464.1	None					165.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(825, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)