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

• Label: 1428.2.bp
• Level: $1428$
• Weight: $2$
• Character orbit: 1428.bp
• Rep. character: $\chi_{1428}(155,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $864$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.bp (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 204 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(576\)

Dimensions

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

	Total	New	Old
Modular forms	1184	864	320
Cusp forms	1120	864	256
Eisenstein series	64	0	64

Trace form

\( 864 q + 16 q^{9} + O(q^{10}) \)

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

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)