Space of modular forms of level 2028, weight 4, and Character 2028.k

• Label: 2028.4.k
• Level: $2028$
• Weight: $4$
• Character orbit: 2028.k
• Rep. character: $\chi_{2028}(775,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $924$
• Sturm bound: $1456$

Defining parameters

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2028.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(1456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2028, [\chi])\).

	Total	New	Old
Modular forms	2240	924	1316
Cusp forms	2128	924	1204
Eisenstein series	112	0	112

Trace form

924 * q + 4 * q^5 - 8316 * q^9 + 416 * q^14 - 144 * q^16 + 460 * q^20 + 120 * q^21 - 88 * q^22 - 180 * q^24 - 416 * q^28 + 1100 * q^32 + 72 * q^34 - 372 * q^37 - 2856 * q^40 + 1772 * q^41 - 936 * q^42 + 1132 * q^44 - 36 * q^45 - 1000 * q^46 + 1248 * q^48 + 344 * q^50 - 424 * q^53 - 504 * q^57 - 1224 * q^58 + 804 * q^60 + 1112 * q^61 - 2544 * q^66 + 2064 * q^68 + 1352 * q^70 + 1276 * q^73 - 1200 * q^74 - 5904 * q^76 - 3236 * q^80 + 74844 * q^81 - 1400 * q^85 - 2064 * q^86 - 2500 * q^89 - 7944 * q^92 - 1848 * q^93 + 4408 * q^94 - 2280 * q^96 - 1188 * q^97 + 1016 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

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