Space of modular forms of level 3392, weight 2, and Character 3392.bf

• Label: 3392.2.bf
• Level: $3392$
• Weight: $2$
• Character orbit: 3392.bf
• Rep. character: $\chi_{3392}(83,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $3440$
• Sturm bound: $864$

Defining parameters

Level:	\( N \)	\(=\)	\( 3392 = 2^{6} \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3392.bf (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3392 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3392, [\chi])\).

	Total	New	Old
Modular forms	3472	3472	0
Cusp forms	3440	3440	0
Eisenstein series	32	32	0

Trace form

3440 * q - 8 * q^2 - 8 * q^3 - 8 * q^5 - 8 * q^8 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^15 - 16 * q^16 + 32 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 24 * q^23 - 16 * q^24 - 8 * q^26 - 8 * q^27 - 16 * q^28 + 88 * q^30 - 16 * q^31 - 8 * q^32 + 8 * q^34 - 8 * q^35 + 144 * q^36 - 8 * q^39 - 8 * q^41 - 16 * q^42 + 32 * q^43 - 16 * q^44 + 16 * q^45 - 16 * q^46 - 16 * q^47 - 8 * q^48 - 16 * q^49 - 8 * q^50 - 16 * q^51 + 128 * q^52 - 8 * q^53 + 112 * q^54 - 8 * q^55 - 144 * q^56 - 8 * q^58 + 56 * q^61 - 16 * q^65 - 16 * q^66 + 72 * q^67 - 16 * q^68 - 16 * q^69 + 144 * q^70 - 8 * q^71 - 8 * q^72 - 8 * q^73 + 136 * q^74 - 48 * q^75 - 72 * q^76 - 16 * q^77 + 136 * q^80 - 16 * q^81 + 72 * q^83 + 144 * q^84 - 48 * q^85 - 8 * q^86 - 8 * q^87 - 16 * q^88 - 16 * q^89 + 56 * q^92 + 72 * q^94 - 32 * q^95 - 48 * q^96 + 32 * q^98 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3392, [\chi])\) into newform subspaces

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