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

• Label: 161.4.i
• Level: $161$
• Weight: $4$
• Character orbit: 161.i
• Rep. character: $\chi_{161}(8,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $360$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
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	360	140
Cusp forms	460	360	100
Eisenstein series	40	0	40

Trace form

360 * q + 2 * q^2 + 8 * q^3 - 130 * q^4 - 16 * q^5 + 6 * q^6 + 14 * q^7 - 24 * q^8 - 388 * q^9 - 120 * q^10 + 108 * q^11 + 50 * q^12 + 112 * q^13 - 14 * q^14 + 852 * q^15 - 138 * q^16 + 208 * q^17 - 168 * q^18 - 180 * q^19 + 124 * q^20 + 84 * q^21 - 624 * q^22 - 670 * q^23 - 3048 * q^24 - 1020 * q^25 - 670 * q^26 + 68 * q^27 - 98 * q^28 + 816 * q^29 + 1416 * q^30 + 836 * q^31 + 786 * q^32 + 1296 * q^33 + 4476 * q^34 - 56 * q^35 + 59 * q^36 + 808 * q^37 + 64 * q^38 - 516 * q^39 - 3940 * q^40 - 708 * q^41 + 168 * q^42 - 2240 * q^43 - 1599 * q^44 + 1032 * q^45 - 8056 * q^46 - 5624 * q^47 - 3242 * q^48 - 1764 * q^49 - 1343 * q^50 - 780 * q^51 + 3574 * q^52 + 952 * q^53 + 7406 * q^54 + 7952 * q^55 + 210 * q^56 + 9556 * q^57 + 5671 * q^58 - 156 * q^59 + 7840 * q^60 + 2960 * q^61 - 4782 * q^62 - 322 * q^63 - 11240 * q^64 + 1640 * q^65 - 6796 * q^66 - 2844 * q^67 + 3936 * q^68 - 7384 * q^69 - 1008 * q^70 - 6576 * q^71 + 2164 * q^72 - 1608 * q^73 + 2041 * q^74 + 17072 * q^75 + 7578 * q^76 + 4284 * q^77 + 2394 * q^78 + 2360 * q^79 + 19480 * q^80 + 4608 * q^81 + 1326 * q^82 + 10036 * q^83 - 3402 * q^84 + 8016 * q^85 - 11048 * q^86 - 484 * q^87 - 1633 * q^88 - 11396 * q^89 - 35186 * q^90 - 8120 * q^91 - 768 * q^92 - 26416 * q^93 - 1198 * q^94 - 6456 * q^95 - 6196 * q^96 + 6564 * q^97 - 441 * q^98 + 516 * 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.i.a	$161$	$4$	161.i	23.c	$11$	$170$	$17$	$9.499$		None		✓			161.4.i.a	$2$	$0$	\(0\)	\(10\)	\(10\)	\(-119\)		$\mathrm{SU}(2)[C_{11}]$
161.4.i.b	$161$	$4$	161.i	23.c	$11$	$190$	$19$	$9.499$		None		✓	✓		161.4.i.b	$2$	$0$	\(2\)	\(-2\)	\(-26\)	\(133\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(161, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(161, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)