Space of modular forms of level 1984, weight 2, and Character 1984.cm

• Label: 1984.2.cm
• Level: $1984$
• Weight: $2$
• Character orbit: 1984.cm
• Rep. character: $\chi_{1984}(49,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $992$
• Sturm bound: $512$

Defining parameters

Level:	\( N \)	\(=\)	\( 1984 = 2^{6} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1984.cm (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 496 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1984, [\chi])\).

	Total	New	Old
Modular forms	4224	1056	3168
Cusp forms	3968	992	2976
Eisenstein series	256	64	192

Trace form

992 * q + 18 * q^3 - 8 * q^5 + 18 * q^11 - 18 * q^13 + 56 * q^15 - 36 * q^17 + 66 * q^19 - 6 * q^21 + 24 * q^27 - 12 * q^29 + 32 * q^31 - 24 * q^33 + 18 * q^35 - 8 * q^37 + 18 * q^43 - 42 * q^45 + 24 * q^47 - 136 * q^49 + 22 * q^51 - 18 * q^53 - 22 * q^59 - 64 * q^61 + 8 * q^63 - 36 * q^65 + 56 * q^67 + 24 * q^69 - 24 * q^75 + 16 * q^77 - 20 * q^79 - 128 * q^81 + 38 * q^83 + 50 * q^85 + 48 * q^91 - 70 * q^93 + 72 * q^95 - 24 * q^97 - 34 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1984, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1984, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1984, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(496, [\chi])\)\(^{\oplus 3}\)