Space of modular forms of level 3528, weight 2, and Character 3528.eq

• Label: 3528.2.eq
• Level: $3528$
• Weight: $2$
• Character orbit: 3528.eq
• Rep. character: $\chi_{3528}(269,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $2688$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3528.eq (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1176 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

	Total	New	Old
Modular forms	8160	2688	5472
Cusp forms	7968	2688	5280
Eisenstein series	192	0	192

Trace form

\( 2688 q + 24 q^{22} - 224 q^{25} + 40 q^{28} - 112 q^{34} - 172 q^{40} + 20 q^{46} - 16 q^{49} - 36 q^{52} + 16 q^{58} + 72 q^{64} + 200 q^{70} - 48 q^{73} + 84 q^{76} - 8 q^{82} + 24 q^{88} + 276 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)