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

• Label: 825.2.d
• Level: $825$
• Weight: $2$
• Character orbit: 825.d
• Rep. character: $\chi_{825}(824,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $6$
• Sturm bound: $240$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(240\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(7\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	132	76	56
Cusp forms	108	68	40
Eisenstein series	24	8	16

Trace form

\( 68 q - 56 q^{4} + 14 q^{9} + O(q^{10}) \)

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.d.a	$825$	$2$	825.d	165.d	$2$	$4$	$4$	$6.588$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+2q^{4}+(2-\beta _{3})q^{9}+\cdots\)
825.2.d.b	$825$	$2$	825.d	165.d	$2$	$8$	$8$	$6.588$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
825.2.d.c	$825$	$2$	825.d	165.d	$2$	$8$	$8$	$6.588$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(-\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)
825.2.d.d	$825$	$2$	825.d	165.d	$2$	$8$	$8$	$6.588$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(\beta _{3}-\beta _{6}+\cdots)q^{3}+\cdots\)
825.2.d.e	$825$	$2$	825.d	165.d	$2$	$8$	$8$	$6.588$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
825.2.d.f	$825$	$2$	825.d	165.d	$2$	$32$	$32$	$6.588$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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