Space of modular forms of level 34, weight 2, and Character 34.c

• Label: 34.2.c
• Level: $34$
• Weight: $2$
• Character orbit: 34.c
• Rep. character: $\chi_{34}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $9$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 34 = 2 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	34.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(9\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(34, [\chi])\).

	Total	New	Old
Modular forms	12	4	8
Cusp forms	4	4	0
Eisenstein series	8	0	8

Trace form

4 * q - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^10 - 6 * q^11 + 2 * q^12 - 4 * q^13 + 4 * q^14 + 4 * q^16 + 6 * q^17 + 4 * q^18 - 2 * q^20 + 8 * q^21 - 10 * q^22 + 8 * q^23 + 2 * q^24 - 8 * q^27 + 4 * q^28 - 10 * q^29 - 8 * q^30 + 4 * q^31 - 4 * q^33 - 6 * q^34 - 16 * q^35 + 6 * q^37 - 16 * q^38 + 12 * q^39 - 6 * q^40 + 4 * q^41 + 6 * q^44 - 2 * q^45 + 8 * q^46 + 32 * q^47 - 2 * q^48 + 12 * q^50 - 6 * q^51 + 4 * q^52 + 8 * q^54 + 24 * q^55 - 4 * q^56 - 8 * q^57 + 2 * q^58 - 26 * q^61 + 20 * q^62 + 4 * q^63 - 4 * q^64 - 32 * q^65 - 28 * q^67 - 6 * q^68 - 16 * q^71 - 4 * q^72 + 8 * q^73 - 6 * q^74 + 6 * q^75 + 12 * q^78 + 2 * q^80 - 8 * q^81 - 8 * q^84 + 22 * q^85 - 4 * q^86 + 10 * q^88 - 10 * q^90 + 24 * q^91 - 8 * q^92 + 24 * q^95 - 2 * q^96 - 4 * q^97 - 16 * q^98 + 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(34, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
34.2.c.a	$34$	$2$	34.c	17.c	$4$	$2$	$1$	$0.271$	\(\Q(\sqrt{-1}) \)	None		✓			34.2.c.a	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-i q^{2}+(-i-1)q^{3}-q^{4}+(2 i+2)q^{5}+\cdots\)
34.2.c.b	$34$	$2$	34.c	17.c	$4$	$2$	$1$	$0.271$	\(\Q(\sqrt{-1}) \)	None		✓			34.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+i q^{2}-q^{4}+(-i-1)q^{5}-i q^{8}+\cdots\)