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

• Label: 1360.2.x
• Level: $1360$
• Weight: $2$
• Character orbit: 1360.x
• Rep. character: $\chi_{1360}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $384$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(432\)

Dimensions

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

	Total	New	Old
Modular forms	440	384	56
Cusp forms	424	384	40
Eisenstein series	16	0	16

Trace form

384 * q + 12 * q^8 - 384 * q^9 - 16 * q^12 - 28 * q^18 - 12 * q^20 + 4 * q^22 + 32 * q^26 + 12 * q^28 - 36 * q^30 - 24 * q^35 - 40 * q^38 - 60 * q^40 - 60 * q^42 + 64 * q^43 - 80 * q^44 + 48 * q^47 - 28 * q^48 - 20 * q^50 + 60 * q^52 + 32 * q^54 - 48 * q^56 + 48 * q^58 + 20 * q^60 + 56 * q^62 + 8 * q^66 - 48 * q^67 + 96 * q^70 - 40 * q^72 - 88 * q^74 - 88 * q^75 + 32 * q^76 + 124 * q^78 - 76 * q^80 + 384 * q^81 + 36 * q^82 + 96 * q^84 + 32 * q^86 - 112 * q^87 + 112 * q^88 + 104 * q^90 + 16 * q^92 - 24 * q^94 + 80 * q^95 + 104 * q^96 - 92 * q^98 + 64 * 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

\( S_{2}^{\mathrm{old}}(1360, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)