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

• Label: 3528.2.eo
• Level: $3528$
• Weight: $2$
• Character orbit: 3528.eo
• Rep. character: $\chi_{3528}(37,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $3336$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3528.eo (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 392 \)
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	3384	4776
Cusp forms	7968	3336	4632
Eisenstein series	192	48	144

Trace form

3336 * q + 13 * q^2 - 13 * q^4 - 24 * q^7 + 4 * q^8 - 6 * q^10 + 55 * q^14 - 17 * q^16 + 26 * q^17 - 18 * q^20 + 6 * q^22 + 26 * q^23 - 296 * q^25 + 18 * q^26 - 38 * q^28 + 60 * q^31 + 3 * q^32 - 50 * q^34 + 20 * q^38 - 68 * q^40 + 20 * q^41 + 26 * q^44 - 2 * q^46 + 34 * q^47 - 32 * q^49 - 96 * q^50 - 34 * q^52 - 32 * q^55 - 56 * q^56 - 16 * q^58 + 72 * q^62 - 4 * q^64 + 36 * q^65 + 27 * q^68 + 68 * q^70 + 100 * q^71 - 34 * q^73 + 34 * q^74 + 47 * q^76 - 12 * q^79 - 34 * q^80 - 8 * q^82 + 121 * q^86 - 145 * q^88 + 18 * q^89 + 82 * q^92 + 46 * q^94 + 88 * q^95 + 219 * q^98

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

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)