Space of modular forms of level 205, weight 2, and Character 205.k

• Label: 205.2.k
• Level: $205$
• Weight: $2$
• Character orbit: 205.k
• Rep. character: $\chi_{205}(16,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $42$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.k (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(42\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(205, [\chi])\).

	Total	New	Old
Modular forms	88	56	32
Cusp forms	72	56	16
Eisenstein series	16	0	16

Trace form

56 * q - 2 * q^2 - 4 * q^3 - 14 * q^4 - 2 * q^5 - 10 * q^6 + 12 * q^8 + 40 * q^9 - 2 * q^10 - 2 * q^11 - 24 * q^12 - 4 * q^13 + 12 * q^14 - 14 * q^16 - 6 * q^17 - 22 * q^18 + 14 * q^19 - 6 * q^20 - 28 * q^21 - 36 * q^22 + 12 * q^23 + 18 * q^24 - 14 * q^25 - 36 * q^26 - 64 * q^27 + 6 * q^28 + 12 * q^29 + 6 * q^30 - 2 * q^31 - 8 * q^32 - 16 * q^33 - 12 * q^34 + 2 * q^35 + 64 * q^36 + 16 * q^37 + 48 * q^38 + 36 * q^39 + 24 * q^40 + 18 * q^41 - 48 * q^42 - 4 * q^43 - 6 * q^45 + 20 * q^46 + 40 * q^47 - 4 * q^48 - 4 * q^49 + 8 * q^50 + 18 * q^51 - 56 * q^52 - 20 * q^53 - 56 * q^54 - 8 * q^55 - 40 * q^56 - 76 * q^57 - 22 * q^58 - 28 * q^59 - 28 * q^60 + 46 * q^61 - 18 * q^62 + 20 * q^63 + 88 * q^64 - 12 * q^65 + 32 * q^66 + 22 * q^67 + 124 * q^68 + 2 * q^69 - 36 * q^70 - 58 * q^71 + 62 * q^72 + 48 * q^73 - 36 * q^74 + 6 * q^75 + 34 * q^76 + 24 * q^77 - 12 * q^78 + 20 * q^79 - 30 * q^80 - 40 * q^81 + 98 * q^82 + 84 * q^83 - 36 * q^84 - 4 * q^85 - 70 * q^86 - 72 * q^87 + 28 * q^88 + 42 * q^89 - 10 * q^90 - 76 * q^91 - 66 * q^92 + 20 * q^93 + 78 * q^94 + 12 * q^95 + 8 * q^96 - 56 * q^97 - 28 * q^98 - 92 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(205, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
205.2.k.a	$205$	$2$	205.k	41.d	$5$	$24$	$6$	$1.637$		None		✓			205.2.k.a	$2$	$0$	\(0\)	\(-2\)	\(6\)	\(-1\)		$\mathrm{SU}(2)[C_{5}]$
205.2.k.b	$205$	$2$	205.k	41.d	$5$	$32$	$8$	$1.637$		None		✓	✓		205.2.k.b	$2$	$0$	\(-2\)	\(-2\)	\(-8\)	\(1\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(205, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)