Space of modular forms of level 49, weight 6, and Character 49.g

• Label: 49.6.g
• Level: $49$
• Weight: $6$
• Character orbit: 49.g
• Rep. character: $\chi_{49}(2,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $264$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(49, [\chi])\).

	Total	New	Old
Modular forms	288	288	0
Cusp forms	264	264	0
Eisenstein series	24	24	0

Trace form

264 * q - 13 * q^2 - 22 * q^3 + 307 * q^4 - 52 * q^5 - 130 * q^6 + 154 * q^7 - 320 * q^8 + 6 * q^9 - 792 * q^10 - 635 * q^11 + 3605 * q^12 + 1834 * q^13 - 875 * q^14 - 2572 * q^15 + 3735 * q^16 - 1023 * q^17 - 1336 * q^18 + 9741 * q^19 + 8330 * q^20 + 1512 * q^21 + 842 * q^22 - 1553 * q^23 + 1756 * q^24 + 13144 * q^25 - 1946 * q^26 - 19849 * q^27 - 31584 * q^28 - 30356 * q^29 + 6129 * q^30 + 43903 * q^31 + 27725 * q^32 - 3412 * q^33 - 73182 * q^34 - 17360 * q^35 - 102868 * q^36 - 22105 * q^37 + 19116 * q^38 + 109165 * q^39 + 77354 * q^40 + 47446 * q^41 + 157738 * q^42 + 6674 * q^43 + 15154 * q^44 - 130923 * q^45 - 136952 * q^46 - 195163 * q^47 - 151484 * q^48 - 131194 * q^49 + 263000 * q^50 - 84276 * q^51 - 58758 * q^52 - 110577 * q^53 + 170313 * q^54 + 290245 * q^55 + 79688 * q^56 + 47310 * q^57 + 252156 * q^58 + 127308 * q^59 + 86254 * q^60 + 166863 * q^61 - 63578 * q^62 - 243033 * q^63 - 293812 * q^64 - 16702 * q^65 - 661788 * q^66 + 46195 * q^67 + 393869 * q^68 + 321394 * q^69 - 64330 * q^70 - 61793 * q^71 + 333944 * q^72 + 21699 * q^73 + 133514 * q^74 - 431136 * q^75 + 3087 * q^76 - 48993 * q^77 - 450576 * q^78 - 181 * q^79 + 264228 * q^80 + 142090 * q^81 - 512442 * q^82 + 102424 * q^83 + 344932 * q^84 - 205502 * q^85 + 611991 * q^86 + 1427200 * q^87 + 685993 * q^88 + 145800 * q^89 + 677844 * q^90 + 732956 * q^91 + 10018 * q^92 - 1233536 * q^93 - 601938 * q^94 - 945265 * q^95 - 2372958 * q^96 - 1932952 * q^97 - 672973 * q^98 + 1090736 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(49, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.6.g.a	$49$	$6$	49.g	49.g	$21$	$264$	$22$	$7.859$		None		✓	✓	✓	49.6.g.a	$2$	$0$	\(-13\)	\(-22\)	\(-52\)	\(154\)		$\mathrm{SU}(2)[C_{21}]$