Space of modular forms of level 2028, weight 2, and Character 2028.w

• Label: 2028.2.w
• Level: $2028$
• Weight: $2$
• Character orbit: 2028.w
• Rep. character: $\chi_{2028}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $616$
• Sturm bound: $728$

Defining parameters

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2028.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2028, [\chi])\).

	Total	New	Old
Modular forms	1568	616	952
Cusp forms	1344	616	728
Eisenstein series	224	0	224

Trace form

616 * q + 4 * q^5 + 308 * q^9 + 32 * q^14 + 16 * q^16 + 52 * q^20 - 8 * q^21 + 4 * q^22 - 12 * q^24 + 28 * q^28 + 80 * q^32 + 24 * q^34 + 12 * q^37 - 72 * q^40 + 56 * q^41 - 12 * q^42 - 56 * q^44 + 8 * q^45 - 36 * q^46 - 16 * q^48 + 72 * q^49 - 52 * q^50 + 56 * q^53 - 108 * q^56 + 48 * q^57 - 56 * q^58 - 16 * q^60 + 36 * q^61 - 60 * q^62 - 32 * q^66 + 48 * q^68 + 16 * q^70 + 76 * q^73 - 48 * q^74 + 12 * q^76 + 4 * q^80 - 308 * q^81 + 60 * q^82 - 4 * q^85 + 12 * q^88 - 100 * q^89 - 168 * q^92 + 8 * q^93 - 36 * q^94 + 40 * q^96 - 36 * q^97 - 148 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2028, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)