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Properties

Label 3528.2.dq
Level $3528$
Weight $2$
Character orbit 3528.dq
Rep. character $\chi_{3528}(253,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1668$
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.dq (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4080 1692 2388
Cusp forms 3984 1668 2316
Eisenstein series 96 24 72

Trace form

\( 1668 q + 5 q^{2} - 5 q^{4} - 12 q^{7} + 11 q^{8} + O(q^{10}) \) \( 1668 q + 5 q^{2} - 5 q^{4} - 12 q^{7} + 11 q^{8} - 3 q^{10} - 25 q^{14} - 13 q^{16} + 10 q^{17} + 15 q^{20} - 21 q^{22} + 10 q^{23} + 260 q^{25} - 9 q^{26} + 44 q^{28} - 96 q^{31} - 15 q^{32} + 71 q^{34} + 19 q^{38} + 5 q^{40} + 10 q^{41} - 29 q^{44} + 29 q^{46} - 34 q^{47} - 4 q^{49} + 132 q^{50} + 13 q^{52} - 46 q^{55} + 62 q^{56} - 11 q^{58} - 3 q^{62} - 11 q^{64} + 30 q^{65} - 12 q^{68} - 41 q^{70} - 70 q^{71} - 26 q^{73} + 59 q^{74} + 10 q^{76} - 24 q^{79} + 28 q^{80} + 92 q^{82} + 95 q^{86} - 59 q^{88} - 6 q^{89} - 46 q^{92} + 116 q^{94} - 16 q^{95} - 24 q^{97} + 105 q^{98} + O(q^{100}) \)

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

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