Space of modular forms of level 820, weight 2, and Character 820.u

• Label: 820.2.u
• Level: $820$
• Weight: $2$
• Character orbit: 820.u
• Rep. character: $\chi_{820}(141,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(252\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(820, [\chi])\).

	Total	New	Old
Modular forms	528	56	472
Cusp forms	480	56	424
Eisenstein series	48	0	48

Trace form

56 * q + 4 * q^3 + 2 * q^5 + 64 * q^9 - 6 * q^11 - 4 * q^13 + 10 * q^17 - 14 * q^19 - 4 * q^21 + 24 * q^23 - 14 * q^25 - 8 * q^27 - 12 * q^29 - 2 * q^31 + 8 * q^33 + 10 * q^35 - 24 * q^37 + 54 * q^41 + 4 * q^43 + 22 * q^45 + 4 * q^47 - 12 * q^49 + 66 * q^51 - 4 * q^53 - 8 * q^55 - 12 * q^57 + 16 * q^59 - 38 * q^61 - 76 * q^63 + 4 * q^65 - 62 * q^67 - 42 * q^69 + 6 * q^71 - 80 * q^73 - 6 * q^75 + 8 * q^77 - 84 * q^79 + 160 * q^81 - 116 * q^83 - 4 * q^85 + 64 * q^87 - 22 * q^89 - 12 * q^91 - 76 * q^93 + 12 * q^95 - 56 * q^97 + 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(820, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
820.2.u.a	$820$	$2$	820.u	41.d	$5$	$24$	$6$	$6.548$		None		✓			820.2.u.a	$2$	$0$	\(0\)	\(2\)	\(-6\)	\(5\)		$\mathrm{SU}(2)[C_{5}]$
820.2.u.b	$820$	$2$	820.u	41.d	$5$	$32$	$8$	$6.548$		None		✓	✓		820.2.u.b	$2$	$0$	\(0\)	\(2\)	\(8\)	\(-5\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(820, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(820, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 2}\)