Space of modular forms of level 3971, weight 2, and Character 3971.bs

• Label: 3971.2.bs
• Level: $3971$
• Weight: $2$
• Character orbit: 3971.bs
• Rep. character: $\chi_{3971}(4,\cdot)$
• Character field: $\Q(\zeta_{855})$
• Dimension: $163296$
• Sturm bound: $760$

Defining parameters

Level:	\( N \)	\(=\)	\( 3971 = 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3971.bs (of order \(855\) and degree \(432\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3971 \)
Character field:			\(\Q(\zeta_{855})\)
Sturm bound:			\(760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3971, [\chi])\).

	Total	New	Old
Modular forms	165024	165024	0
Cusp forms	163296	163296	0
Eisenstein series	1728	1728	0

Trace form

163296 * q - 324 * q^2 - 318 * q^3 - 324 * q^4 - 324 * q^5 - 333 * q^6 - 333 * q^7 - 315 * q^8 - 306 * q^9 - 864 * q^10 - 444 * q^11 - 888 * q^12 - 324 * q^13 - 276 * q^14 - 348 * q^15 - 312 * q^16 - 342 * q^18 - 324 * q^19 - 396 * q^20 - 846 * q^21 - 540 * q^22 - 864 * q^23 - 351 * q^24 - 324 * q^25 - 345 * q^26 - 453 * q^27 - 300 * q^28 - 315 * q^29 - 333 * q^30 - 339 * q^31 - 810 * q^32 - 594 * q^33 - 972 * q^34 - 282 * q^35 - 498 * q^36 - 282 * q^37 - 510 * q^38 - 306 * q^39 - 162 * q^40 - 336 * q^41 - 435 * q^42 - 327 * q^44 - 924 * q^45 - 333 * q^46 - 348 * q^47 + 1422 * q^48 - 1443 * q^49 - 339 * q^50 - 264 * q^51 - 309 * q^52 - 315 * q^53 - 2022 * q^54 - 288 * q^55 - 660 * q^56 - 414 * q^57 - 234 * q^58 - 447 * q^59 - 465 * q^60 - 336 * q^61 - 396 * q^62 - 282 * q^63 - 1425 * q^64 - 1116 * q^65 - 225 * q^66 - 918 * q^67 - 204 * q^68 - 180 * q^69 - 183 * q^70 - 330 * q^71 - 414 * q^72 - 414 * q^73 - 564 * q^74 - 306 * q^75 - 1068 * q^76 - 438 * q^77 - 1254 * q^78 - 324 * q^79 - 372 * q^80 - 126 * q^81 - 369 * q^82 - 351 * q^83 - 459 * q^84 - 324 * q^85 - 288 * q^86 - 984 * q^87 - 450 * q^88 - 990 * q^89 - 408 * q^90 + 126 * q^91 - 192 * q^92 - 432 * q^93 - 708 * q^94 - 846 * q^95 - 450 * q^96 - 369 * q^97 - 1038 * q^98 - 537 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3971, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.