Space of modular forms of level 1428, weight 2, and Character 1428.s

• Label: 1428.2.s
• Level: $1428$
• Weight: $2$
• Character orbit: 1428.s
• Rep. character: $\chi_{1428}(55,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $288$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 476 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

	Total	New	Old
Modular forms	592	288	304
Cusp forms	560	288	272
Eisenstein series	32	0	32

Trace form

\( 288 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)