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

• Label: 825.2.f
• Level: $825$
• Weight: $2$
• Character orbit: 825.f
• Rep. character: $\chi_{825}(626,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $7$
• Sturm bound: $240$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(240\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(23\), \(37\)

Dimensions

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

	Total	New	Old
Modular forms	132	82	50
Cusp forms	108	70	38
Eisenstein series	24	12	12

Trace form

\( 70 q + 3 q^{3} + 68 q^{4} - 7 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
825.2.f.a	$825$	$2$	825.f	33.d	$2$	$2$	$2$	$6.588$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}-2q^{4}+(-3+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
825.2.f.b	$825$	$2$	825.f	33.d	$2$	$4$	$4$	$6.588$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}-2q^{4}+(3+\beta _{2})q^{9}+(1+2\beta _{2}+\cdots)q^{11}+\cdots\)
825.2.f.c	$825$	$2$	825.f	33.d	$2$	$8$	$8$	$6.588$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{2}+(-\beta _{3}-\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
825.2.f.d	$825$	$2$	825.f	33.d	$2$	$8$	$8$	$6.588$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
825.2.f.e	$825$	$2$	825.f	33.d	$2$	$16$	$16$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{1})q^{4}+\beta _{5}q^{6}+\cdots\)
825.2.f.f	$825$	$2$	825.f	33.d	$2$	$16$	$16$	$6.588$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-\beta _{5}q^{3}+(2-\beta _{2})q^{4}+\beta _{14}q^{6}+\cdots\)
825.2.f.g	$825$	$2$	825.f	33.d	$2$	$16$	$16$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{1})q^{4}-\beta _{5}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \)