Space of modular forms of level 3168, weight 2, and Character 3168.ew

• Label: 3168.2.ew
• Level: $3168$
• Weight: $2$
• Character orbit: 3168.ew
• Rep. character: $\chi_{3168}(157,\cdot)$
• Character field: $\Q(\zeta_{120})$
• Dimension: $18304$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 3168 = 2^{5} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3168.ew (of order \(120\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3168 \)
Character field:			\(\Q(\zeta_{120})\)
Sturm bound:			\(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3168, [\chi])\).

	Total	New	Old
Modular forms	18560	18560	0
Cusp forms	18304	18304	0
Eisenstein series	256	256	0

Trace form

18304 * q - 12 * q^2 - 24 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 12 * q^7 - 48 * q^8 - 24 * q^9 - 128 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 12 * q^14 - 12 * q^16 - 24 * q^18 - 48 * q^19 - 12 * q^20 - 64 * q^21 - 16 * q^22 - 32 * q^23 - 24 * q^24 - 12 * q^25 - 48 * q^26 - 24 * q^27 - 48 * q^28 - 12 * q^29 - 8 * q^30 - 24 * q^31 - 32 * q^32 - 64 * q^33 - 48 * q^34 - 48 * q^35 - 24 * q^36 - 48 * q^37 - 12 * q^38 - 24 * q^39 - 12 * q^40 - 12 * q^41 + 16 * q^42 - 32 * q^43 + 24 * q^44 - 64 * q^45 - 48 * q^46 - 24 * q^48 - 12 * q^50 - 72 * q^51 - 12 * q^52 - 48 * q^53 + 24 * q^54 - 64 * q^55 - 352 * q^56 - 24 * q^57 - 12 * q^58 - 12 * q^59 + 8 * q^60 - 12 * q^61 - 80 * q^62 - 48 * q^63 - 48 * q^64 - 64 * q^65 - 104 * q^66 - 32 * q^67 - 44 * q^68 - 24 * q^69 - 12 * q^70 - 48 * q^71 - 204 * q^72 - 48 * q^73 - 12 * q^74 + 16 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 144 * q^80 - 48 * q^82 - 12 * q^83 - 136 * q^84 - 52 * q^85 - 220 * q^86 - 64 * q^87 - 16 * q^88 - 128 * q^89 + 96 * q^90 - 48 * q^91 + 140 * q^92 - 48 * q^93 + 20 * q^94 + 232 * q^95 + 40 * q^96 - 24 * q^97 - 96 * q^98 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3168, [\chi])\) into newform subspaces

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