Space of modular forms of level 1521, weight 2, and Character 1521.h

• Label: 1521.2.h
• Level: $1521$
• Weight: $2$
• Character orbit: 1521.h
• Rep. character: $\chi_{1521}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $288$
• Sturm bound: $364$

Defining parameters

Level:	\( N \)	\(=\)	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1521.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1521, [\chi])\).

	Total	New	Old
Modular forms	392	328	64
Cusp forms	336	288	48
Eisenstein series	56	40	16

Trace form

\( 288 q + 2 q^{2} + q^{3} + 270 q^{4} + 2 q^{5} + 12 q^{6} - 3 q^{7} + 18 q^{8} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1521, [\chi]) \cong \)