Space of modular forms of level 1870, weight 4, and Character 1870.bp

• Label: 1870.4.bp
• Level: $1870$
• Weight: $4$
• Character orbit: 1870.bp
• Rep. character: $\chi_{1870}(109,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $2592$
• Sturm bound: $1296$

Defining parameters

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1870.bp (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 935 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1870, [\chi])\).

	Total	New	Old
Modular forms	7840	2592	5248
Cusp forms	7712	2592	5120
Eisenstein series	128	0	128

Trace form

\( 2592 q + 448 q^{11} - 1792 q^{25} - 1728 q^{31} + 256 q^{44} - 6144 q^{49} + 1424 q^{55} - 19968 q^{69} + 8064 q^{70} - 768 q^{75} + 2048 q^{80} - 13824 q^{81} + 5248 q^{86} + 9216 q^{91} + 11776 q^{99}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1870, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)