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Properties

Label 3528.2.ff
Level $3528$
Weight $2$
Character orbit 3528.ff
Rep. character $\chi_{3528}(257,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2016$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.ff (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
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 2016 6144
Cusp forms 7968 2016 5952
Eisenstein series 192 0 192

Trace form

\( 2016 q - 10 q^{9} + O(q^{10}) \) \( 2016 q - 10 q^{9} - 8 q^{21} + 168 q^{25} + 18 q^{27} - 18 q^{29} + 6 q^{39} - 6 q^{41} + 6 q^{43} + 106 q^{45} + 90 q^{47} - 6 q^{49} - 12 q^{51} - 12 q^{53} + 42 q^{55} + 8 q^{57} - 46 q^{63} - 84 q^{69} - 240 q^{75} + 36 q^{77} + 12 q^{79} - 50 q^{81} - 32 q^{87} - 18 q^{89} - 6 q^{91} + 144 q^{93} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)