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Properties

Label 3528.2.ea
Level $3528$
Weight $2$
Character orbit 3528.ea
Rep. character $\chi_{3528}(185,\cdot)$
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.ea (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

\( 2016 q + 26 q^{9} + O(q^{10}) \) \( 2016 q + 26 q^{9} + 10 q^{21} - 336 q^{25} - 18 q^{27} + 108 q^{29} - 18 q^{31} - 12 q^{33} - 12 q^{39} + 6 q^{41} + 6 q^{43} - 38 q^{45} - 18 q^{47} + 12 q^{49} + 6 q^{51} + 12 q^{53} + 42 q^{55} + 8 q^{57} - 18 q^{61} + 32 q^{63} - 84 q^{69} + 84 q^{75} + 12 q^{77} - 6 q^{79} + 46 q^{81} - 2 q^{87} + 18 q^{89} - 6 q^{91} + 180 q^{93} + 54 q^{95} + 36 q^{99} + O(q^{100}) \)

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

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