↑

Properties

Label 3528.2.q
Level $3528$
Weight $2$
Character orbit 3528.q
Rep. character $\chi_{3528}(1537,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $240$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1408 240 1168
Cusp forms 1280 240 1040
Eisenstein series 128 0 128

Trace form

\( 240 q - 4 q^{5} - 4 q^{9} + O(q^{10}) \) \( 240 q - 4 q^{5} - 4 q^{9} + 16 q^{15} - 8 q^{17} + 8 q^{23} - 120 q^{25} + 6 q^{27} + 6 q^{29} + 12 q^{31} - 8 q^{33} + 46 q^{39} - 18 q^{41} - 6 q^{43} + 2 q^{45} + 12 q^{47} - 60 q^{51} - 4 q^{53} - 12 q^{55} + 32 q^{57} - 72 q^{59} + 12 q^{61} + 48 q^{65} + 32 q^{69} + 64 q^{71} - 30 q^{75} - 12 q^{79} + 12 q^{81} + 36 q^{83} + 68 q^{87} - 18 q^{89} - 16 q^{93} - 4 q^{95} + 84 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \)