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

• Label: 825.2.p
• Level: $825$
• Weight: $2$
• Character orbit: 825.p
• Rep. character: $\chi_{825}(181,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $240$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.p (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	496	240	256
Cusp forms	464	240	224
Eisenstein series	32	0	32

Trace form

240 * q - 60 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^7 + 240 * q^9 - 2 * q^10 + 6 * q^11 + 4 * q^12 - 8 * q^13 + 2 * q^15 - 56 * q^16 + 2 * q^17 - 14 * q^19 + 4 * q^20 - 8 * q^21 + 30 * q^22 - 32 * q^23 - 12 * q^24 + 12 * q^25 + 10 * q^26 + 14 * q^28 - 16 * q^30 + 2 * q^31 + 60 * q^32 + 14 * q^33 + 8 * q^35 - 60 * q^36 + 10 * q^37 + 84 * q^38 + 64 * q^39 - 84 * q^40 + 6 * q^41 + 2 * q^42 - 48 * q^43 - 44 * q^44 + 6 * q^45 - 32 * q^46 - 64 * q^47 - 32 * q^48 - 52 * q^49 + 6 * q^50 - 16 * q^51 - 28 * q^52 + 6 * q^53 - 4 * q^54 - 36 * q^55 - 12 * q^57 - 18 * q^58 + 6 * q^59 + 20 * q^60 + 72 * q^61 - 80 * q^62 + 4 * q^63 - 16 * q^64 - 34 * q^65 + 12 * q^66 + 44 * q^67 - 26 * q^68 + 2 * q^69 - 104 * q^70 - 24 * q^71 + 34 * q^73 + 22 * q^74 + 8 * q^75 + 188 * q^76 - 6 * q^77 - 24 * q^78 - 38 * q^79 - 72 * q^80 + 240 * q^81 + 76 * q^82 - 136 * q^83 - 24 * q^84 - 4 * q^85 - 28 * q^86 - 40 * q^87 + 126 * q^88 - 2 * q^90 + 40 * q^92 + 72 * q^93 - 34 * q^94 + 90 * q^95 + 112 * q^96 - 80 * q^97 - 184 * q^98 + 6 * q^99

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.p.a	$825$	$2$	825.p	275.k	$5$	$4$	$1$	$6.588$	\(\Q(\zeta_{10})\)	None		✓			825.2.p.a	$2$	$1$	\(-5\)	\(4\)	\(-5\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2+2\zeta_{10}+\zeta_{10}^{3})q^{2}+q^{3}-3\zeta_{10}q^{4}+\cdots\)
825.2.p.b	$825$	$2$	825.p	275.k	$5$	$116$	$29$	$6.588$		None		✓			825.2.p.b	$2$	$0$	\(3\)	\(116\)	\(9\)	\(-3\)		$\mathrm{SU}(2)[C_{5}]$
825.2.p.c	$825$	$2$	825.p	275.k	$5$	$120$	$30$	$6.588$		None		✓	✓		825.2.p.c	$2$	$0$	\(2\)	\(-120\)	\(2\)	\(6\)		$\mathrm{SU}(2)[C_{5}]$

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

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