Space of modular forms of level 49, weight 7, and Character 49.f

• Label: 49.7.f
• Level: $49$
• Weight: $7$
• Character orbit: 49.f
• Rep. character: $\chi_{49}(6,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $162$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.f (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(49, [\chi])\).

	Total	New	Old
Modular forms	174	174	0
Cusp forms	162	162	0
Eisenstein series	12	12	0

Trace form

162 * q - 5 * q^2 - 7 * q^3 - 837 * q^4 - 7 * q^5 - 791 * q^6 + 70 * q^7 - 843 * q^8 + 2990 * q^9 - 7 * q^10 + 1171 * q^11 - 13482 * q^12 - 7 * q^13 + 22533 * q^14 + 6181 * q^15 - 17901 * q^16 - 3143 * q^17 - 22692 * q^18 + 50169 * q^20 + 28553 * q^21 - 33057 * q^22 - 49677 * q^23 - 119077 * q^24 + 30038 * q^25 + 59577 * q^26 + 11753 * q^27 + 42994 * q^28 + 80383 * q^29 + 27328 * q^30 + 253875 * q^32 - 7 * q^33 + 54677 * q^34 - 74067 * q^35 - 193099 * q^36 + 118463 * q^37 - 121079 * q^38 - 304143 * q^39 - 702079 * q^40 - 58023 * q^41 - 1137479 * q^42 + 93963 * q^43 + 352505 * q^44 + 1333577 * q^45 + 782877 * q^46 + 408261 * q^47 - 149338 * q^49 + 1164004 * q^50 - 911743 * q^51 + 721273 * q^52 - 992325 * q^53 - 576646 * q^54 - 1502935 * q^55 + 1368514 * q^56 + 116032 * q^57 + 2610717 * q^58 + 24493 * q^59 - 1027131 * q^60 + 563101 * q^61 - 262199 * q^62 - 966154 * q^63 - 2839067 * q^64 - 140287 * q^65 - 1523319 * q^66 - 1313660 * q^67 + 2216753 * q^69 + 1806959 * q^70 + 1031011 * q^71 - 3123354 * q^72 - 846727 * q^73 + 1270357 * q^74 + 873173 * q^75 + 5463990 * q^76 + 1565235 * q^77 + 1006005 * q^78 + 82420 * q^79 + 2259538 * q^81 - 7672672 * q^82 - 3860031 * q^83 - 9104942 * q^84 + 1596833 * q^85 + 224039 * q^86 + 2590525 * q^87 + 4179421 * q^88 + 5417433 * q^89 + 6759578 * q^90 - 6163507 * q^91 - 7060306 * q^92 + 1903160 * q^93 + 4029998 * q^94 + 2115400 * q^95 + 957950 * q^96 - 1546783 * q^98 + 4449580 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(49, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.7.f.a	$49$	$7$	49.f	49.f	$14$	$162$	$27$	$11.273$		None		✓	✓	✓	49.7.f.a	$2$	$0$	\(-5\)	\(-7\)	\(-7\)	\(70\)		$\mathrm{SU}(2)[C_{14}]$