Space of modular forms of level 3328, weight 2, and Character 3328.db

• Label: 3328.2.db
• Level: $3328$
• Weight: $2$
• Character orbit: 3328.db
• Rep. character: $\chi_{3328}(15,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $1760$
• Sturm bound: $896$

Defining parameters

Level:	\( N \)	\(=\)	\( 3328 = 2^{8} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3328.db (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 832 \)
Character field:			\(\Q(\zeta_{48})\)
Sturm bound:			\(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3328, [\chi])\).

	Total	New	Old
Modular forms	7296	1824	5472
Cusp forms	7040	1760	5280
Eisenstein series	256	64	192

Trace form

1760 * q + 8 * q^3 - 16 * q^5 + 16 * q^7 - 8 * q^9 + 16 * q^11 - 16 * q^13 + 24 * q^15 - 24 * q^17 + 16 * q^19 - 16 * q^21 + 24 * q^23 + 32 * q^27 - 8 * q^29 + 32 * q^31 + 8 * q^35 - 16 * q^37 - 80 * q^39 - 16 * q^41 + 24 * q^43 - 40 * q^45 - 24 * q^49 - 32 * q^53 + 72 * q^55 - 16 * q^57 - 48 * q^59 - 8 * q^61 - 32 * q^65 + 16 * q^67 - 24 * q^69 - 48 * q^71 - 16 * q^73 - 16 * q^75 + 32 * q^79 - 8 * q^81 + 16 * q^83 + 64 * q^85 + 8 * q^87 - 16 * q^89 + 16 * q^91 + 8 * q^93 + 48 * q^95 + 296 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3328, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3328, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3328, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 3}\)