Space of modular forms of level 2070, weight 2, and Character 2070.i

• Label: 2070.2.i
• Level: $2070$
• Weight: $2$
• Character orbit: 2070.i
• Rep. character: $\chi_{2070}(691,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $176$
• Sturm bound: $864$

Defining parameters

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2070, [\chi])\).

	Total	New	Old
Modular forms	880	176	704
Cusp forms	848	176	672
Eisenstein series	32	0	32

Trace form

176 * q - 4 * q^2 - 4 * q^3 - 88 * q^4 - 4 * q^6 - 8 * q^7 + 8 * q^8 + 12 * q^9 + 12 * q^11 + 8 * q^12 - 8 * q^13 - 8 * q^15 - 88 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 8 * q^21 + 12 * q^22 - 4 * q^24 - 88 * q^25 + 8 * q^27 + 16 * q^28 - 16 * q^29 - 8 * q^31 - 4 * q^32 + 4 * q^33 + 12 * q^34 + 16 * q^35 - 12 * q^36 + 16 * q^37 + 4 * q^38 + 8 * q^39 + 4 * q^41 + 4 * q^43 - 24 * q^44 - 4 * q^48 - 96 * q^49 - 4 * q^50 - 12 * q^51 - 8 * q^52 - 4 * q^54 + 4 * q^57 + 4 * q^59 - 8 * q^60 - 56 * q^61 + 64 * q^62 - 32 * q^63 + 176 * q^64 + 8 * q^65 + 56 * q^66 - 44 * q^67 + 4 * q^68 - 80 * q^71 - 4 * q^72 + 88 * q^73 - 4 * q^75 + 4 * q^76 - 32 * q^77 + 32 * q^78 + 16 * q^79 + 44 * q^81 - 24 * q^82 + 24 * q^83 + 16 * q^84 + 24 * q^85 + 36 * q^86 - 104 * q^87 + 12 * q^88 - 64 * q^89 + 80 * q^91 + 16 * q^93 + 8 * q^96 + 4 * q^97 + 8 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2070, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)