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

• Label: 49.7.h
• Level: $49$
• Weight: $7$
• Character orbit: 49.h
• Rep. character: $\chi_{49}(3,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $324$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.h (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{42})\)
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	348	348	0
Cusp forms	324	324	0
Eisenstein series	24	24	0

Trace form

324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * 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.h.a	$49$	$7$	49.h	49.h	$42$	$324$	$27$	$11.273$		None		✓	✓	✓	49.7.h.a	$2$	$0$	\(-13\)	\(-11\)	\(-179\)	\(392\)		$\mathrm{SU}(2)[C_{42}]$