Space of modular forms of level 49, weight 10, and Character 49.g

• Label: 49.10.g
• Level: $49$
• Weight: $10$
• Character orbit: 49.g
• Rep. character: $\chi_{49}(2,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $492$
• Newform subspaces: $1$
• Sturm bound: $46$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(46\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(49, [\chi])\).

	Total	New	Old
Modular forms	516	516	0
Cusp forms	492	492	0
Eisenstein series	24	24	0

Trace form

492 * q - 13 * q^2 - 175 * q^3 + 10227 * q^4 - 1547 * q^5 - 7210 * q^6 + 1022 * q^7 - 320 * q^8 + 391050 * q^9 - 4312 * q^10 + 1653 * q^11 + 58037 * q^12 + 319662 * q^13 - 1195467 * q^14 - 256642 * q^15 + 2222263 * q^16 - 1381303 * q^17 + 317000 * q^18 + 3665102 * q^19 - 1685110 * q^20 + 1557843 * q^21 - 7202382 * q^22 - 7716057 * q^23 - 22244852 * q^24 + 13169494 * q^25 - 6856290 * q^26 + 15865430 * q^27 + 13957104 * q^28 + 11313264 * q^29 - 10941711 * q^30 + 19608638 * q^31 - 8028195 * q^32 - 1689373 * q^33 + 3298274 * q^34 + 7005495 * q^35 - 81250036 * q^36 - 3928945 * q^37 - 6129508 * q^38 - 31920098 * q^39 - 189080486 * q^40 + 8770566 * q^41 + 156673426 * q^42 - 104392746 * q^43 + 94053106 * q^44 - 136658928 * q^45 - 119216056 * q^46 - 263332125 * q^47 - 855307964 * q^48 - 209918520 * q^49 + 623579800 * q^50 + 100907439 * q^51 + 1077988058 * q^52 + 576733781 * q^53 + 575013705 * q^54 + 752005590 * q^55 + 303064328 * q^56 - 260958111 * q^57 - 1263176500 * q^58 - 607181113 * q^59 - 1125559106 * q^60 + 539172711 * q^61 + 353205398 * q^62 - 386135358 * q^63 - 1936011572 * q^64 + 114603188 * q^65 + 1158459540 * q^66 + 88578470 * q^67 + 1763772941 * q^68 - 429961616 * q^69 + 2016816270 * q^70 - 737795936 * q^71 + 532298216 * q^72 + 848662885 * q^73 - 246677726 * q^74 - 2280262236 * q^75 - 4265778993 * q^76 - 2571860669 * q^77 - 560655984 * q^78 + 218512512 * q^79 + 4473121828 * q^80 + 8514093433 * q^81 + 8612009462 * q^82 - 720267282 * q^83 - 5659288124 * q^84 - 1216605272 * q^85 - 4194477537 * q^86 - 392646842 * q^87 + 5036020249 * q^88 - 1786507331 * q^89 + 11463153324 * q^90 + 4096670172 * q^91 - 1873029662 * q^92 + 6883772248 * q^93 - 10001180042 * q^94 - 4744369480 * q^95 - 35098550046 * q^96 + 2854332852 * q^97 - 14215587197 * q^98 + 9994213436 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(49, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.10.g.a	$49$	$10$	49.g	49.g	$21$	$492$	$41$	$25.237$		None		✓	✓	✓	49.10.g.a	$2$	$0$	\(-13\)	\(-175\)	\(-1547\)	\(1022\)		$\mathrm{SU}(2)[C_{21}]$