Space of modular forms of level 1976, weight 2, and Character 1976.q

• Label: 1976.2.q
• Level: $1976$
• Weight: $2$
• Character orbit: 1976.q
• Rep. character: $\chi_{1976}(1569,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $140$
• Sturm bound: $560$

Defining parameters

Level:	\( N \)	\(=\)	\( 1976 = 2^{3} \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1976.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 247 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1976, [\chi])\).

	Total	New	Old
Modular forms	576	140	436
Cusp forms	544	140	404
Eisenstein series	32	0	32

Trace form

140 * q - 4 * q^3 - 2 * q^7 - 70 * q^9 + 2 * q^11 + 2 * q^13 + 16 * q^15 + 4 * q^17 - 2 * q^21 - 70 * q^25 + 32 * q^27 - 20 * q^29 - 12 * q^33 - 4 * q^35 + 4 * q^37 - 2 * q^39 + 12 * q^41 + 16 * q^43 + 24 * q^45 - 4 * q^47 - 74 * q^49 - 24 * q^51 + 18 * q^53 - 12 * q^55 + 2 * q^57 - 16 * q^59 + 4 * q^61 + 8 * q^63 + 12 * q^65 + 28 * q^67 + 14 * q^69 - 4 * q^71 + 30 * q^73 - 28 * q^75 - 8 * q^77 - 18 * q^79 - 54 * q^81 + 8 * q^85 + 14 * q^87 + 12 * q^89 - 32 * q^91 + 4 * q^93 + 12 * q^95 + 4 * q^97 + 10 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1976, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1976, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1976, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(247, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(494, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(988, [\chi])\)\(^{\oplus 2}\)