Space of modular forms of level 17, weight 4, and trivial character

• Label: 17.4.a
• Level: $17$
• Weight: $4$
• Character orbit: 17.a
• Rep. character: $\chi_{17}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(6\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(17))\).

	Total	New	Old
Modular forms	6	4	2
Cusp forms	4	4	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.

\(17\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(2\)	\(1\)	\(1\)		\(1\)	\(1\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

4 * q - 2 * q^2 - 4 * q^3 + 26 * q^4 - 2 * q^5 - 50 * q^6 - 6 * q^7 - 18 * q^8 + 96 * q^9 - 74 * q^10 - 52 * q^11 + 14 * q^12 - 28 * q^13 + 176 * q^14 + 60 * q^15 + 66 * q^16 - 34 * q^17 - 214 * q^18 + 196 * q^19 - 162 * q^20 + 32 * q^21 + 358 * q^22 + 82 * q^23 - 834 * q^24 - 312 * q^25 + 200 * q^26 - 100 * q^27 + 448 * q^28 - 426 * q^29 + 544 * q^30 + 58 * q^31 - 26 * q^32 - 140 * q^33 - 68 * q^34 - 500 * q^35 + 1350 * q^36 + 298 * q^37 + 376 * q^38 + 732 * q^39 - 298 * q^40 - 636 * q^41 - 1800 * q^42 + 408 * q^43 - 1146 * q^44 - 162 * q^45 - 524 * q^46 + 928 * q^47 + 1342 * q^48 + 172 * q^49 + 814 * q^50 - 204 * q^51 - 832 * q^52 + 620 * q^53 - 860 * q^54 - 68 * q^55 + 96 * q^56 - 1648 * q^57 - 1394 * q^58 + 888 * q^59 + 1280 * q^60 + 26 * q^61 + 1024 * q^62 + 86 * q^63 - 486 * q^64 + 60 * q^65 + 1892 * q^66 + 524 * q^67 - 408 * q^68 + 1056 * q^69 - 1000 * q^70 - 1110 * q^71 - 150 * q^72 + 1200 * q^73 + 1010 * q^74 - 836 * q^75 - 792 * q^76 + 168 * q^77 - 84 * q^78 - 1078 * q^79 - 466 * q^80 - 864 * q^81 + 1384 * q^82 - 1640 * q^83 - 1816 * q^84 + 238 * q^85 - 820 * q^86 + 1188 * q^87 + 1334 * q^88 - 944 * q^89 - 2674 * q^90 + 608 * q^91 + 4836 * q^92 + 2008 * q^93 - 2880 * q^94 + 224 * q^95 + 318 * q^96 - 652 * q^97 + 1534 * q^98 - 3808 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\) 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
17.4.a.a	$17$	$4$	17.a	1.a	$1$	$1$	$1$	$1.003$	\(\Q\)	None	✓	✓	✓	✓	17.4.a.a	$1$	$1$	\(-3\)	\(-8\)	\(6\)	\(-28\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b	$17$	$4$	17.a	1.a	$1$	$3$	$3$	$1.003$	3.3.2636.1	None	✓	✓	✓	✓	17.4.a.b	$1$	$0$	\(1\)	\(4\)	\(-8\)	\(22\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)