Space of modular forms of level 1360, weight 2, and Character 1360.fa

• Label: 1360.2.fa
• Level: $1360$
• Weight: $2$
• Character orbit: 1360.fa
• Rep. character: $\chi_{1360}(97,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $416$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.fa (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1360, [\chi])\).

	Total	New	Old
Modular forms	1824	448	1376
Cusp forms	1632	416	1216
Eisenstein series	192	32	160

Trace form

416 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 + 16 * q^11 - 16 * q^13 + 8 * q^15 - 8 * q^17 - 32 * q^19 - 16 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 + 16 * q^31 + 16 * q^35 - 8 * q^37 + 48 * q^39 - 16 * q^41 + 8 * q^43 - 8 * q^45 + 16 * q^51 - 16 * q^53 + 56 * q^55 - 8 * q^57 - 16 * q^61 + 128 * q^63 - 48 * q^65 - 96 * q^67 + 16 * q^71 + 32 * q^73 + 8 * q^75 - 8 * q^77 - 16 * q^81 + 56 * q^83 - 8 * q^85 + 8 * q^87 + 16 * q^91 + 56 * q^93 + 8 * q^95 - 8 * q^97 + 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1360, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1360, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(680, [\chi])\)\(^{\oplus 2}\)