Space of modular forms of level 3871, weight 2, and Character 3871.v

• Label: 3871.2.v
• Level: $3871$
• Weight: $2$
• Character orbit: 3871.v
• Rep. character: $\chi_{3871}(1079,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $3228$
• Sturm bound: $746$

Defining parameters

Level:	\( N \)	\(=\)	\( 3871 = 7^{2} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3871.v (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{13})\)
Sturm bound:			\(746\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3871, [\chi])\).

	Total	New	Old
Modular forms	4560	3348	1212
Cusp forms	4368	3228	1140
Eisenstein series	192	120	72

Trace form

3228 * q + 9 * q^2 + 9 * q^3 - 253 * q^4 + 11 * q^5 + 9 * q^6 - 39 * q^8 - 254 * q^9 + 15 * q^10 + 31 * q^11 - 7 * q^12 + 3 * q^13 - 53 * q^15 - 247 * q^16 + 3 * q^17 + 68 * q^18 + 9 * q^19 + 18 * q^20 - 36 * q^22 + 10 * q^23 + 94 * q^24 - 180 * q^25 - 6 * q^26 + 36 * q^27 - 59 * q^29 + 57 * q^30 + 35 * q^31 - 61 * q^32 - q^33 - 32 * q^34 - 337 * q^36 + 57 * q^37 + 29 * q^38 + 119 * q^39 - 22 * q^40 + 3 * q^41 - 39 * q^43 + 129 * q^44 - 15 * q^45 - 205 * q^46 + 31 * q^47 + 29 * q^48 - 50 * q^50 + q^51 - 73 * q^52 + 57 * q^53 - 95 * q^54 + 18 * q^55 + 77 * q^57 - 19 * q^58 + 51 * q^59 + 94 * q^60 + 13 * q^61 + 12 * q^62 - 301 * q^64 - 15 * q^65 + 83 * q^66 - 77 * q^67 - 97 * q^68 + 62 * q^69 - 97 * q^71 - 86 * q^72 + 28 * q^73 - 28 * q^74 - 45 * q^75 + 274 * q^76 - 106 * q^78 + 78 * q^79 - 408 * q^80 - 210 * q^81 - 19 * q^82 - 113 * q^83 - 103 * q^85 + 218 * q^86 - 38 * q^87 + 225 * q^88 - 3 * q^89 - 99 * q^90 + 4 * q^92 - 17 * q^93 - 165 * q^94 + 51 * q^95 - 145 * q^96 + 136 * q^97 - 152 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3871, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3871, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3871, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(553, [\chi])\)\(^{\oplus 2}\)