Space of modular forms of level 1710, weight 2, and Character 1710.cp

• Label: 1710.2.cp
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.cp
• Rep. character: $\chi_{1710}(41,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $480$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.cp (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1710, [\chi])\).

	Total	New	Old
Modular forms	2208	480	1728
Cusp forms	2112	480	1632
Eisenstein series	96	0	96

Trace form

480 * q + 12 * q^3 + 12 * q^6 - 12 * q^9 - 12 * q^13 - 12 * q^19 + 18 * q^22 - 6 * q^24 + 18 * q^27 - 12 * q^28 - 60 * q^33 - 12 * q^36 - 12 * q^39 + 12 * q^43 + 6 * q^48 - 240 * q^49 + 24 * q^51 - 24 * q^52 + 36 * q^54 + 24 * q^57 + 180 * q^59 - 84 * q^61 + 48 * q^63 - 240 * q^64 + 30 * q^66 - 204 * q^67 + 18 * q^68 + 6 * q^72 + 48 * q^73 - 72 * q^78 + 24 * q^79 - 156 * q^81 + 18 * q^82 + 144 * q^83 + 12 * q^87 + 108 * q^89 - 24 * q^90 + 24 * q^91 - 36 * q^97 - 66 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1710, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)