Space of modular forms of level 17, weight 6, and trivial character

• Label: 17.6.a
• Level: $17$
• Weight: $6$
• Character orbit: 17.a
• Rep. character: $\chi_{17}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $9$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(9\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(17))\).

	Total	New	Old
Modular forms	8	6	2
Cusp forms	6	6	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(17\)	Dim
\(+\)	\(2\)
\(-\)	\(4\)

Trace form

6 * q - 2 * q^2 + 20 * q^3 + 42 * q^4 - 8 * q^5 + 106 * q^6 + 116 * q^7 - 66 * q^8 + 6 * q^9 - 262 * q^10 - 100 * q^11 - 586 * q^12 + 412 * q^13 - 472 * q^14 - 1176 * q^15 - 1166 * q^16 + 578 * q^17 + 1682 * q^18 + 1040 * q^19 + 438 * q^20 + 752 * q^21 - 2702 * q^22 + 4660 * q^23 + 2958 * q^24 + 7474 * q^25 - 5584 * q^26 + 3608 * q^27 + 1424 * q^28 - 4824 * q^29 - 9488 * q^30 - 1956 * q^31 - 4394 * q^32 - 9512 * q^33 + 2312 * q^34 + 8056 * q^35 - 20682 * q^36 - 672 * q^37 - 13352 * q^38 - 19896 * q^39 + 14678 * q^40 + 45108 * q^41 + 49464 * q^42 - 16576 * q^43 + 25758 * q^44 - 24264 * q^45 + 32900 * q^46 - 32720 * q^47 - 42434 * q^48 + 3718 * q^49 + 5110 * q^50 + 10404 * q^51 + 79968 * q^52 - 100180 * q^53 + 17260 * q^54 - 7688 * q^55 - 94032 * q^56 - 880 * q^57 + 162706 * q^58 + 61824 * q^59 - 88480 * q^60 + 62304 * q^61 - 46856 * q^62 + 91316 * q^63 - 76918 * q^64 - 133296 * q^65 - 77764 * q^66 - 26840 * q^67 + 27744 * q^68 + 91680 * q^69 - 257352 * q^70 + 107100 * q^71 - 72822 * q^72 - 145332 * q^73 + 69230 * q^74 + 351820 * q^75 + 248024 * q^76 - 200016 * q^77 + 262836 * q^78 - 51676 * q^79 + 205502 * q^80 - 144354 * q^81 - 269840 * q^82 - 5600 * q^83 - 111640 * q^84 + 48552 * q^85 + 223460 * q^86 - 255768 * q^87 + 142838 * q^88 - 112532 * q^89 - 300814 * q^90 + 264328 * q^91 + 386628 * q^92 + 279952 * q^93 - 329376 * q^94 + 257072 * q^95 - 186978 * q^96 + 150564 * q^97 - 241298 * q^98 - 310948 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(17))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		17
17.6.a.a	$17$	$6$	17.a	1.a	$1$	$1$	$1$	$2.727$	\(\Q\)	None	✓	✓			17.6.a.a	$1$	$1$	\(-6\)	\(10\)	\(-72\)	\(-196\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}+10q^{3}+4q^{4}-72q^{5}-60q^{6}+\cdots\)
17.6.a.b	$17$	$6$	17.a	1.a	$1$	$1$	$1$	$2.727$	\(\Q\)	None	✓	✓			17.6.a.b	$1$	$1$	\(1\)	\(-18\)	\(-16\)	\(28\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-18q^{3}-31q^{4}-2^{4}q^{5}-18q^{6}+\cdots\)
17.6.a.c	$17$	$6$	17.a	1.a	$1$	$4$	$4$	$2.727$	4.4.5416116.1	None	✓	✓	✓	✓	17.6.a.c	$1$	$0$	\(3\)	\(28\)	\(80\)	\(284\)		$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(7+\beta _{1}-\beta _{3})q^{3}+(18+\cdots)q^{4}+\cdots\)