Space of modular forms of level 161, weight 4, and Character 161.k

• Label: 161.4.k
• Level: $161$
• Weight: $4$
• Character orbit: 161.k
• Rep. character: $\chi_{161}(20,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $460$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.k (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(161, [\chi])\).

	Total	New	Old
Modular forms	500	500	0
Cusp forms	460	460	0
Eisenstein series	40	40	0

Trace form

460 * q - 16 * q^2 - 184 * q^4 - 11 * q^7 - 4 * q^8 + 416 * q^9 - 22 * q^11 - 11 * q^14 - 22 * q^15 - 1136 * q^16 - 32 * q^18 - 671 * q^21 + 422 * q^23 - 960 * q^25 + 341 * q^28 - 258 * q^29 - 1518 * q^30 + 1584 * q^32 - 297 * q^35 + 5555 * q^36 + 1166 * q^37 - 1454 * q^39 + 3619 * q^42 - 1738 * q^43 - 3157 * q^44 + 942 * q^46 + 1705 * q^49 - 3801 * q^50 - 682 * q^51 - 22 * q^53 - 9394 * q^56 + 3806 * q^57 + 5731 * q^58 - 22 * q^60 + 2079 * q^63 - 2100 * q^64 - 8646 * q^65 - 22 * q^67 + 8394 * q^70 + 194 * q^71 - 7166 * q^72 - 2387 * q^74 + 3893 * q^77 + 11314 * q^78 + 3674 * q^79 - 6416 * q^81 - 11363 * q^84 - 3794 * q^85 + 10450 * q^86 + 14421 * q^88 - 14556 * q^92 + 2724 * q^93 + 13358 * q^95 + 2719 * q^98 - 23122 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(161, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
161.4.k.a	$161$	$4$	161.k	161.k	$22$	$20$	$2$	$9.499$	20.0.\(\cdots\).2	\(\Q(\sqrt{-7}) \)		✓			161.4.k.a	$4$	$0$	\(-10\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{22}]$	\(q+(-3-\beta _{2}-3\beta _{3}-3\beta _{5}+3\beta _{6}-3\beta _{8}+\cdots)q^{2}+\cdots\)
161.4.k.b	$161$	$4$	161.k	161.k	$22$	$440$	$44$	$9.499$		None		✓	✓		161.4.k.b	$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-11\)		$\mathrm{SU}(2)[C_{22}]$