Space of modular forms of level 1666, weight 2, and Character 1666.k

• Label: 1666.2.k
• Level: $1666$
• Weight: $2$
• Character orbit: 1666.k
• Rep. character: $\chi_{1666}(239,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $432$
• Sturm bound: $504$

Defining parameters

Level:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.k (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1666, [\chi])\).

	Total	New	Old
Modular forms	1536	432	1104
Cusp forms	1488	432	1056
Eisenstein series	48	0	48

Trace form

432 * q + 4 * q^3 - 72 * q^4 + 4 * q^5 - 16 * q^6 + 12 * q^7 - 84 * q^9 + 12 * q^10 + 8 * q^11 + 4 * q^12 + 16 * q^13 + 8 * q^14 - 20 * q^15 - 72 * q^16 + 4 * q^17 + 8 * q^18 + 40 * q^19 + 4 * q^20 + 24 * q^21 - 20 * q^22 + 12 * q^24 - 48 * q^25 - 12 * q^26 + 16 * q^27 + 12 * q^28 - 20 * q^29 + 8 * q^30 + 40 * q^31 + 56 * q^33 + 4 * q^34 + 12 * q^35 - 84 * q^36 - 56 * q^37 + 8 * q^38 - 60 * q^39 - 16 * q^40 + 56 * q^41 - 88 * q^42 + 40 * q^43 - 20 * q^44 - 160 * q^45 - 52 * q^46 - 80 * q^47 - 24 * q^48 + 40 * q^49 + 40 * q^50 - 40 * q^52 - 112 * q^53 - 36 * q^54 - 132 * q^55 - 20 * q^56 + 96 * q^57 - 80 * q^58 + 36 * q^59 - 20 * q^60 - 104 * q^61 + 40 * q^62 - 96 * q^63 - 72 * q^64 + 56 * q^65 + 72 * q^66 + 64 * q^67 - 24 * q^68 + 36 * q^69 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 4 * q^73 - 4 * q^74 + 132 * q^75 + 40 * q^76 + 36 * q^77 + 32 * q^78 + 80 * q^79 - 24 * q^80 + 8 * q^81 + 24 * q^82 + 20 * q^83 + 24 * q^84 - 36 * q^86 + 4 * q^87 + 8 * q^88 - 116 * q^89 + 84 * q^90 - 80 * q^91 + 64 * q^93 - 76 * q^94 + 64 * q^95 + 12 * q^96 - 136 * q^97 + 20 * q^98 + 80 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1666, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)