Space of modular forms of level 1701, weight 2, and Character 1701.by

• Label: 1701.2.by
• Level: $1701$
• Weight: $2$
• Character orbit: 1701.by
• Rep. character: $\chi_{1701}(5,\cdot)$
• Character field: $\Q(\zeta_{162})$
• Dimension: $11556$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 1701 = 3^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1701.by (of order \(162\) and degree \(54\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1701 \)
Character field:			\(\Q(\zeta_{162})\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1701, [\chi])\).

	Total	New	Old
Modular forms	11772	11772	0
Cusp forms	11556	11556	0
Eisenstein series	216	216	0

Trace form

11556 * q - 27 * q^2 - 81 * q^3 - 27 * q^4 - 81 * q^5 - 54 * q^7 - 108 * q^8 - 27 * q^9 - 81 * q^10 - 27 * q^11 - 81 * q^12 - 54 * q^14 - 108 * q^15 - 27 * q^16 - 81 * q^17 - 27 * q^18 - 81 * q^19 - 54 * q^21 - 108 * q^22 - 27 * q^23 - 81 * q^24 - 27 * q^25 - 81 * q^26 - 54 * q^28 - 108 * q^29 - 27 * q^30 - 81 * q^31 - 27 * q^32 - 81 * q^33 - 54 * q^35 - 108 * q^36 - 27 * q^37 - 81 * q^38 - 27 * q^39 - 81 * q^40 - 54 * q^42 - 108 * q^43 - 27 * q^44 - 81 * q^45 - 27 * q^46 - 81 * q^47 - 54 * q^49 - 108 * q^50 - 27 * q^51 - 81 * q^52 - 27 * q^53 - 81 * q^54 - 54 * q^56 - 108 * q^57 - 27 * q^58 - 81 * q^59 - 27 * q^60 - 81 * q^61 - 54 * q^63 - 108 * q^64 + 81 * q^65 - 81 * q^66 - 27 * q^67 - 81 * q^68 - 54 * q^70 - 216 * q^71 - 351 * q^72 - 81 * q^73 - 27 * q^74 - 81 * q^75 - 486 * q^77 - 324 * q^78 - 27 * q^79 - 81 * q^80 - 27 * q^81 - 81 * q^82 + 324 * q^84 - 108 * q^85 + 405 * q^86 - 81 * q^87 - 27 * q^88 - 81 * q^89 - 54 * q^91 - 432 * q^92 - 135 * q^93 - 81 * q^94 - 27 * q^95 - 81 * q^96 - 270 * q^98 - 162 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1701, [\chi])\) into newform subspaces

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