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Properties

Label 3528.2.p
Level $3528$
Weight $2$
Character orbit 3528.p
Rep. character $\chi_{3528}(3331,\cdot)$
Character field $\Q$
Dimension $196$
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.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 704 204 500
Cusp forms 640 196 444
Eisenstein series 64 8 56

Trace form

\( 196 q + 4 q^{4} + O(q^{10}) \) \( 196 q + 4 q^{4} - 12 q^{11} + 12 q^{16} - 16 q^{22} + 184 q^{25} + 20 q^{32} - 16 q^{43} + 28 q^{44} + 12 q^{46} - 40 q^{50} + 4 q^{58} + 28 q^{64} - 24 q^{65} - 12 q^{67} + 36 q^{74} + 28 q^{86} + 20 q^{88} + 124 q^{92} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)