Space of modular forms of level 801, weight 2, and Character 801.m

• Label: 801.2.m
• Level: $801$
• Weight: $2$
• Character orbit: 801.m
• Rep. character: $\chi_{801}(64,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $360$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 801 = 3^{2} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	801.m (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 89 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(801, [\chi])\).

	Total	New	Old
Modular forms	940	380	560
Cusp forms	860	360	500
Eisenstein series	80	20	60

Trace form

360 * q + 9 * q^2 - 43 * q^4 + 9 * q^5 - 9 * q^7 + 5 * q^8 - 20 * q^10 + 18 * q^11 - 5 * q^13 + 58 * q^14 - 35 * q^16 + 42 * q^17 + 3 * q^19 - 3 * q^20 + 95 * q^22 + 17 * q^23 + 15 * q^25 + 7 * q^26 - 25 * q^28 - 6 * q^29 - 3 * q^31 + 52 * q^32 - 64 * q^34 - 22 * q^35 - 14 * q^37 + 12 * q^38 + 28 * q^40 - 45 * q^41 + 69 * q^43 - 21 * q^44 + 67 * q^46 - 42 * q^47 - 15 * q^49 + 39 * q^50 - 16 * q^52 + 76 * q^53 - 102 * q^55 - 36 * q^56 - 5 * q^58 - q^59 + 39 * q^61 - 52 * q^62 - 131 * q^64 - 25 * q^65 + 9 * q^67 + 108 * q^68 - 10 * q^70 + q^71 - 4 * q^73 - 32 * q^74 - 92 * q^76 + 126 * q^77 - 25 * q^79 - 251 * q^80 + 101 * q^82 - 12 * q^83 - 46 * q^85 - 107 * q^86 - 100 * q^88 + 39 * q^89 + 5 * q^91 - 154 * q^92 - 115 * q^94 - 82 * q^95 - 31 * q^97 - 94 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(801, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
801.2.m.a	$801$	$2$	801.m	89.e	$11$	$60$	$6$	$6.396$		None					89.2.e.a	$2$	$0$	\(7\)	\(0\)	\(1\)	\(-9\)		$\mathrm{SU}(2)[C_{11}]$
801.2.m.b	$801$	$2$	801.m	89.e	$11$	$80$	$8$	$6.396$		None					267.2.i.a	$2$	$0$	\(1\)	\(0\)	\(4\)	\(-2\)		$\mathrm{SU}(2)[C_{11}]$
801.2.m.c	$801$	$2$	801.m	89.e	$11$	$80$	$8$	$6.396$		None					267.2.i.b	$2$	$0$	\(1\)	\(0\)	\(4\)	\(2\)		$\mathrm{SU}(2)[C_{11}]$
801.2.m.d	$801$	$2$	801.m	89.e	$11$	$140$	$14$	$6.396$		None		✓	✓		801.2.m.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(801, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(801, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(89, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(267, [\chi])\)\(^{\oplus 2}\)