Space of modular forms of level 49, weight 4, and Character 49.g

• Label: 49.4.g
• Level: $49$
• Weight: $4$
• Character orbit: 49.g
• Rep. character: $\chi_{49}(2,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $156$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(49, [\chi])\).

	Total	New	Old
Modular forms	180	180	0
Cusp forms	156	156	0
Eisenstein series	24	24	0

Trace form

156 * q - 13 * q^2 - 7 * q^3 + 35 * q^4 - 7 * q^5 - 70 * q^6 - 42 * q^7 + 16 * q^8 + 198 * q^9 + 85 * q^11 - 427 * q^12 + 14 * q^13 - 203 * q^14 + 230 * q^15 + 127 * q^16 + 189 * q^17 - 16 * q^18 - 490 * q^19 - 406 * q^20 + 231 * q^21 + 590 * q^22 - 377 * q^23 - 812 * q^24 + 142 * q^25 + 490 * q^26 + 14 * q^27 - 280 * q^28 + 172 * q^29 - 39 * q^30 - 1162 * q^31 - 1099 * q^32 - 49 * q^33 + 882 * q^34 + 847 * q^35 + 812 * q^36 - 377 * q^37 - 1596 * q^38 - 770 * q^39 - 1694 * q^40 - 938 * q^41 - 3290 * q^42 - 10 * q^43 + 4354 * q^44 + 1176 * q^45 + 3408 * q^46 + 1379 * q^47 + 9604 * q^48 + 2576 * q^49 - 6184 * q^50 + 2271 * q^51 + 6874 * q^52 + 1905 * q^53 + 1617 * q^54 - 1834 * q^55 + 1736 * q^56 + 2673 * q^57 - 4716 * q^58 + 63 * q^59 - 10850 * q^60 - 2625 * q^61 - 4298 * q^62 - 1806 * q^63 - 2756 * q^64 - 196 * q^65 + 2100 * q^66 - 202 * q^67 - 5635 * q^68 - 3248 * q^69 + 6650 * q^70 + 2608 * q^71 - 6424 * q^72 - 2471 * q^73 + 2582 * q^74 + 3612 * q^75 - 4529 * q^76 - 1281 * q^77 + 5040 * q^78 - 608 * q^79 - 12348 * q^80 - 17375 * q^81 - 3234 * q^82 - 9842 * q^83 - 11564 * q^84 - 512 * q^85 - 2301 * q^86 + 2254 * q^87 + 4033 * q^88 + 4977 * q^89 + 18312 * q^90 - 8932 * q^91 + 7714 * q^92 + 14164 * q^93 + 2506 * q^94 + 11504 * q^95 + 12642 * q^96 + 11116 * q^97 + 29771 * q^98 - 10804 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(49, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.4.g.a	$49$	$4$	49.g	49.g	$21$	$156$	$13$	$2.891$		None		✓	✓	✓	49.4.g.a	$2$	$0$	\(-13\)	\(-7\)	\(-7\)	\(-42\)		$\mathrm{SU}(2)[C_{21}]$