Space of modular forms of level 3872, weight 2, and Character 3872.bn

• Label: 3872.2.bn
• Level: $3872$
• Weight: $2$
• Character orbit: 3872.bn
• Rep. character: $\chi_{3872}(245,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $6784$
• Sturm bound: $1056$

Defining parameters

Level:	\( N \)	\(=\)	\( 3872 = 2^{5} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3872.bn (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 352 \)
Character field:			\(\Q(\zeta_{40})\)
Sturm bound:			\(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3872, [\chi])\).

	Total	New	Old
Modular forms	8640	7040	1600
Cusp forms	8256	6784	1472
Eisenstein series	384	256	128

Trace form

6784 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 12 * q^5 + 12 * q^6 + 12 * q^7 + 12 * q^8 + 12 * q^9 + 32 * q^10 - 96 * q^12 + 12 * q^13 + 44 * q^14 + 52 * q^16 - 48 * q^18 + 12 * q^19 + 44 * q^20 + 32 * q^21 - 112 * q^23 + 12 * q^24 + 12 * q^25 + 72 * q^26 + 12 * q^27 + 12 * q^28 + 12 * q^29 + 28 * q^30 + 24 * q^31 - 8 * q^32 - 152 * q^34 + 12 * q^35 + 12 * q^36 + 12 * q^37 + 12 * q^38 + 12 * q^39 - 28 * q^40 + 12 * q^41 + 92 * q^42 + 48 * q^43 - 104 * q^45 + 76 * q^46 + 12 * q^48 + 12 * q^50 + 36 * q^51 + 28 * q^52 - 36 * q^53 + 120 * q^54 - 504 * q^56 + 12 * q^57 + 12 * q^58 - 52 * q^59 - 212 * q^60 + 12 * q^61 - 4 * q^62 - 56 * q^63 + 156 * q^64 + 64 * q^65 - 208 * q^67 + 100 * q^68 + 12 * q^69 - 84 * q^70 - 52 * q^71 - 168 * q^72 + 12 * q^73 + 44 * q^74 + 148 * q^75 + 32 * q^76 - 176 * q^78 + 188 * q^80 + 92 * q^82 + 12 * q^83 - 100 * q^84 + 52 * q^85 - 92 * q^86 + 32 * q^87 - 128 * q^89 + 180 * q^90 - 132 * q^91 - 132 * q^92 - 12 * q^93 - 8 * q^94 + 152 * q^95 + 76 * q^96 + 24 * q^97 + 48 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(3872, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3872, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3872, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)