Space of modular forms of level 1968, weight 2, and Character 1968.bd

• Label: 1968.2.bd
• Level: $1968$
• Weight: $2$
• Character orbit: 1968.bd
• Rep. character: $\chi_{1968}(565,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $336$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 1968 = 2^{4} \cdot 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1968.bd (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 656 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1968, [\chi])\).

	Total	New	Old
Modular forms	680	336	344
Cusp forms	664	336	328
Eisenstein series	16	0	16

Trace form

336 * q - 336 * q^9 + 8 * q^12 - 12 * q^14 - 20 * q^22 - 12 * q^24 - 20 * q^26 + 4 * q^28 - 8 * q^30 + 48 * q^31 + 32 * q^34 + 48 * q^35 + 28 * q^38 - 32 * q^39 + 40 * q^42 + 32 * q^43 + 20 * q^44 + 60 * q^52 - 48 * q^56 - 28 * q^58 - 20 * q^60 - 96 * q^62 - 24 * q^64 + 16 * q^65 - 48 * q^67 + 28 * q^68 - 100 * q^70 + 32 * q^73 + 32 * q^75 - 28 * q^76 + 24 * q^78 + 64 * q^80 + 336 * q^81 - 20 * q^82 + 48 * q^87 + 12 * q^88 + 16 * q^89 - 48 * q^92 - 56 * q^94 + 48 * q^95 + 40 * q^96 + 56 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1968, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1968, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1968, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(656, [\chi])\)\(^{\oplus 2}\)