Space of modular forms of level 1064, weight 2, and Character 1064.cn

• Label: 1064.2.cn
• Level: $1064$
• Weight: $2$
• Character orbit: 1064.cn
• Rep. character: $\chi_{1064}(837,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $288$
• Sturm bound: $320$

Defining parameters

Level:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.cn (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1064, [\chi])\).

	Total	New	Old
Modular forms	328	288	40
Cusp forms	312	288	24
Eisenstein series	16	0	16

Trace form

288 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 144 * q^9 - 10 * q^12 + 26 * q^14 - 18 * q^16 - 16 * q^20 - 40 * q^22 - 8 * q^23 - 32 * q^24 + 144 * q^25 + 16 * q^26 - 44 * q^28 - 36 * q^30 + 32 * q^32 - 64 * q^34 + 20 * q^36 - 12 * q^40 - 18 * q^42 + 20 * q^44 + 4 * q^46 - 40 * q^47 - 32 * q^48 + 24 * q^50 + 70 * q^52 + 18 * q^54 - 64 * q^55 + 30 * q^56 + 8 * q^58 - 12 * q^60 + 72 * q^62 - 80 * q^63 + 52 * q^64 + 56 * q^66 - 32 * q^68 + 8 * q^70 - 80 * q^71 + 10 * q^72 - 18 * q^74 - 100 * q^78 + 40 * q^79 - 100 * q^80 - 160 * q^81 - 4 * q^82 - 112 * q^84 - 28 * q^86 + 48 * q^87 + 18 * q^88 + 16 * q^89 - 152 * q^90 + 64 * q^92 - 54 * q^94 - 8 * q^96 - 32 * q^97 - 58 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1064, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1064, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)