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

• Label: 825.2.bx
• Level: $825$
• Weight: $2$
• Character orbit: 825.bx
• Rep. character: $\chi_{825}(49,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $144$
• Newform subspaces: $10$
• Sturm bound: $240$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(240\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	528	144	384
Cusp forms	432	144	288
Eisenstein series	96	0	96

Trace form

\( 144 q + 36 q^{4} - 4 q^{6} + 36 q^{9} + O(q^{10}) \)

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.bx.a	$825$	$2$	825.bx	55.j	$10$	$8$	$2$	$6.588$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(-\zeta_{20}+\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
825.2.bx.b	$825$	$2$	825.bx	55.j	$10$	$8$	$2$	$6.588$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(-\zeta_{20}+\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
825.2.bx.c	$825$	$2$	825.bx	55.j	$10$	$8$	$2$	$6.588$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(-\zeta_{20}+\cdots)q^{3}+\cdots\)
825.2.bx.d	$825$	$2$	825.bx	55.j	$10$	$8$	$2$	$6.588$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(2\zeta_{20}+\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\zeta_{20}^{3}q^{3}+\cdots\)
825.2.bx.e	$825$	$2$	825.bx	55.j	$10$	$16$	$4$	$6.588$	\(\Q(\zeta_{60})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\zeta_{60}^{11}-\zeta_{60}^{13})q^{2}+(\zeta_{60}-\zeta_{60}^{11}+\cdots)q^{3}+\cdots\)
825.2.bx.f	$825$	$2$	825.bx	55.j	$10$	$16$	$4$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{11}-\beta _{13})q^{2}-\beta _{15}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots\)
825.2.bx.g	$825$	$2$	825.bx	55.j	$10$	$16$	$4$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{10}q^{2}+\beta _{11}q^{3}+(2\beta _{2}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
825.2.bx.h	$825$	$2$	825.bx	55.j	$10$	$16$	$4$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\beta _{8}+\beta _{13}-2\beta _{15})q^{2}-\beta _{14}q^{3}+\cdots\)
825.2.bx.i	$825$	$2$	825.bx	55.j	$10$	$16$	$4$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{15}q^{2}+\beta _{9}q^{3}+(2-2\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
825.2.bx.j	$825$	$2$	825.bx	55.j	$10$	$32$	$8$	$6.588$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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