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

• Label: 825.2.bi
• Level: $825$
• Weight: $2$
• Character orbit: 825.bi
• Rep. character: $\chi_{825}(101,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $280$
• Newform subspaces: $8$
• Sturm bound: $240$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bi (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(240\)
Trace bound:			\(4\)
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	528	328	200
Cusp forms	432	280	152
Eisenstein series	96	48	48

Trace form

\( 280 q + 2 q^{3} - 58 q^{4} - 10 q^{6} + 10 q^{7} + 2 q^{9} + O(q^{10}) \)

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.bi.a	$825$	$2$	825.bi	33.f	$10$	$8$	$2$	$6.588$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(-1+\zeta_{20}+\cdots)q^{3}+\cdots\)
825.2.bi.b	$825$	$2$	825.bi	33.f	$10$	$8$	$2$	$6.588$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(1+\zeta_{20}-\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
825.2.bi.c	$825$	$2$	825.bi	33.f	$10$	$8$	$2$	$6.588$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(1+\zeta_{20}-\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
825.2.bi.d	$825$	$2$	825.bi	33.f	$10$	$16$	$4$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(10\)	$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\)
825.2.bi.e	$825$	$2$	825.bi	33.f	$10$	$48$	$12$	$6.588$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{10}]$
825.2.bi.f	$825$	$2$	825.bi	33.f	$10$	$56$	$14$	$6.588$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
825.2.bi.g	$825$	$2$	825.bi	33.f	$10$	$56$	$14$	$6.588$		None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
825.2.bi.h	$825$	$2$	825.bi	33.f	$10$	$80$	$20$	$6.588$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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