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

• Label: 3528.2.w
• Level: $3528$
• Weight: $2$
• Character orbit: 3528.w
• Rep. character: $\chi_{3528}(949,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $944$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3528.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	1376	976	400
Cusp forms	1312	944	368
Eisenstein series	64	32	32

Trace form

944 * q - q^2 - q^4 + 2 * q^6 - 16 * q^8 + 2 * q^9 - 2 * q^10 + 17 * q^12 - 22 * q^15 - q^16 + 4 * q^17 - q^18 - 6 * q^20 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 876 * q^25 + 4 * q^26 + 20 * q^30 - 2 * q^31 - 11 * q^32 - 22 * q^33 - 4 * q^36 - 10 * q^38 + 14 * q^39 - 8 * q^40 + 4 * q^41 + 7 * q^44 - 6 * q^46 - 42 * q^47 + 3 * q^48 + 45 * q^50 + 18 * q^52 + 58 * q^54 - 4 * q^55 - 4 * q^57 + 10 * q^58 + 24 * q^60 - 32 * q^62 - 16 * q^64 - 22 * q^65 - 79 * q^66 - 24 * q^68 - 32 * q^71 + 23 * q^72 + 4 * q^73 - 14 * q^74 + 6 * q^76 + 13 * q^78 - 2 * q^79 + 11 * q^80 - 6 * q^81 - 66 * q^86 - 4 * q^87 - 14 * q^88 - 4 * q^89 + 35 * q^90 + 70 * q^92 - 9 * q^94 + 38 * q^95 + 16 * q^96 + 4 * q^97

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

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)