Space of modular forms of level 34, weight 4, and Character 34.c

• Label: 34.4.c
• Level: $34$
• Weight: $4$
• Character orbit: 34.c
• Rep. character: $\chi_{34}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 34 = 2 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(34, [\chi])\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	24	8	16
Eisenstein series	8	0	8

Trace form

8 * q - 2 * q^3 - 32 * q^4 - 26 * q^5 - 20 * q^6 - 8 * q^7 - 4 * q^10 + 162 * q^11 + 8 * q^12 + 116 * q^13 - 40 * q^14 + 128 * q^16 - 102 * q^17 - 400 * q^18 + 104 * q^20 + 304 * q^21 + 236 * q^22 - 44 * q^23 + 80 * q^24 - 608 * q^27 + 32 * q^28 - 246 * q^29 + 240 * q^30 - 480 * q^31 - 284 * q^33 - 84 * q^34 - 1240 * q^35 + 378 * q^37 + 1056 * q^38 + 628 * q^39 + 16 * q^40 + 920 * q^41 - 648 * q^44 + 2642 * q^45 + 48 * q^46 - 1152 * q^47 - 32 * q^48 - 1088 * q^50 + 458 * q^51 - 464 * q^52 - 352 * q^54 - 848 * q^55 + 160 * q^56 - 1600 * q^57 - 108 * q^58 + 1194 * q^61 + 136 * q^62 + 2304 * q^63 - 512 * q^64 + 1512 * q^65 - 132 * q^67 + 408 * q^68 - 2040 * q^69 - 436 * q^71 + 1600 * q^72 + 636 * q^73 + 468 * q^74 - 1106 * q^75 - 2648 * q^78 + 1500 * q^79 - 416 * q^80 - 5796 * q^81 - 664 * q^82 - 1216 * q^84 + 26 * q^85 - 776 * q^86 - 944 * q^88 + 264 * q^89 + 5788 * q^90 - 1000 * q^91 + 176 * q^92 + 1968 * q^95 - 320 * q^96 + 544 * q^97 + 456 * q^98 + 3670 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(34, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
34.4.c.a	$34$	$4$	34.c	17.c	$4$	$2$	$1$	$2.006$	\(\Q(\sqrt{-1}) \)	None		✓			34.4.c.a	$2$	$0$	\(0\)	\(-6\)	\(-14\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-2 i q^{2}+(-3 i-3)q^{3}-4 q^{4}+\cdots\)
34.4.c.b	$34$	$4$	34.c	17.c	$4$	$6$	$3$	$2.006$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓	✓		34.4.c.b	$2$	$0$	\(0\)	\(4\)	\(-12\)	\(-14\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+2\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}-4q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(34, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(34, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)