Space of modular forms of level 3381, weight 2, and Character 3381.bh

• Label: 3381.2.bh
• Level: $3381$
• Weight: $2$
• Character orbit: 3381.bh
• Rep. character: $\chi_{3381}(361,\cdot)$
• Character field: $\Q(\zeta_{33})$
• Dimension: $3200$
• Sturm bound: $896$

Defining parameters

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.bh (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{33})\)
Sturm bound:			\(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3381, [\chi])\).

	Total	New	Old
Modular forms	9280	3200	6080
Cusp forms	8640	3200	5440
Eisenstein series	640	0	640

Trace form

3200 * q - 8 * q^2 + 152 * q^4 + 4 * q^5 + 48 * q^8 + 160 * q^9 - 8 * q^10 - 4 * q^11 + 224 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 + 144 * q^20 + 64 * q^22 + 80 * q^23 + 220 * q^25 + 28 * q^26 + 88 * q^29 + 4 * q^31 + 52 * q^32 - 8 * q^33 - 16 * q^34 - 392 * q^36 + 48 * q^37 + 196 * q^38 - 36 * q^40 - 32 * q^41 - 120 * q^43 + 252 * q^44 + 4 * q^45 - 24 * q^46 + 4 * q^47 - 32 * q^48 - 608 * q^50 + 80 * q^51 + 216 * q^52 - 48 * q^53 - 32 * q^55 - 144 * q^57 - 8 * q^58 + 92 * q^59 + 20 * q^60 + 52 * q^61 + 96 * q^62 - 112 * q^64 + 32 * q^65 - 16 * q^66 - 16 * q^67 - 12 * q^68 - 16 * q^69 - 24 * q^72 + 24 * q^73 - 12 * q^74 + 16 * q^75 + 32 * q^76 + 16 * q^78 - 68 * q^79 - 122 * q^80 + 160 * q^81 + 152 * q^82 + 80 * q^83 + 432 * q^85 + 72 * q^86 + 12 * q^87 - 532 * q^88 - 32 * q^89 + 16 * q^90 + 284 * q^92 - 48 * q^93 - 194 * q^94 + 270 * q^95 + 20 * q^96 + 16 * q^97 + 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3381, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3381, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)