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

• Label: 205.2.j
• Level: $205$
• Weight: $2$
• Character orbit: 205.j
• Rep. character: $\chi_{205}(9,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $42$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	44	44	0
Cusp forms	36	36	0
Eisenstein series	8	8	0

Trace form

36 * q + 20 * q^4 - 8 * q^6 + 4 * q^10 - 24 * q^14 - 18 * q^15 - 12 * q^16 + 8 * q^19 - 28 * q^24 + 20 * q^25 - 4 * q^26 - 36 * q^29 + 14 * q^30 + 24 * q^31 + 8 * q^34 - 18 * q^35 - 16 * q^40 + 20 * q^41 - 16 * q^44 - 8 * q^45 - 24 * q^51 + 68 * q^54 - 6 * q^55 - 52 * q^56 + 32 * q^59 - 82 * q^60 - 52 * q^64 - 8 * q^65 - 40 * q^66 + 12 * q^69 - 18 * q^70 - 4 * q^71 + 12 * q^75 + 68 * q^76 + 28 * q^79 - 20 * q^81 - 4 * q^85 + 144 * q^86 + 16 * q^89 - 124 * q^94 - 2 * q^95 + 20 * q^96 + 88 * 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.j.a	$205$	$2$	205.j	205.j	$4$	$4$	$2$	$1.637$	\(\Q(i, \sqrt{5})\)	None		✓			205.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+3q^{4}+\beta _{3}q^{5}+\cdots\)
205.2.j.b	$205$	$2$	205.j	205.j	$4$	$8$	$4$	$1.637$	8.0.309760000.3	None		✓			205.2.j.b	$2$	$0$	\(-4\)	\(2\)	\(-4\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{2})q^{2}+(\beta _{2}-\beta _{5})q^{3}-\beta _{2}q^{4}+\cdots\)
205.2.j.c	$205$	$2$	205.j	205.j	$4$	$8$	$4$	$1.637$	8.0.309760000.3	None		✓			205.2.j.b	$2$	$0$	\(4\)	\(-2\)	\(4\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{2})q^{2}+(-\beta _{2}+\beta _{5})q^{3}-\beta _{2}q^{4}+\cdots\)
205.2.j.d	$205$	$2$	205.j	205.j	$4$	$16$	$8$	$1.637$	16.0.\(\cdots\).1	None		✓	✓		205.2.j.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}-\beta _{9}q^{3}+(1+\beta _{5}+\beta _{9}+2\beta _{11}+\cdots)q^{4}+\cdots\)