Properties

Label 1710.2.dh
Level 17101710
Weight 22
Character orbit 1710.dh
Rep. character χ1710(47,)\chi_{1710}(47,\cdot)
Character field Q(ζ36)\Q(\zeta_{36})
Dimension 14401440
Sturm bound 720720

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Defining parameters

Level: N N == 1710=232519 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1710.dh (of order 3636 and degree 1212)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 855 855
Character field: Q(ζ36)\Q(\zeta_{36})
Sturm bound: 720720

Dimensions

The following table gives the dimensions of various subspaces of M2(1710,[χ])M_{2}(1710, [\chi]).

Total New Old
Modular forms 4416 1440 2976
Cusp forms 4224 1440 2784
Eisenstein series 192 0 192

Trace form

1440q+72q15+108q17+24q18+72q2336q33+72q45+24q51216q57+24q6036q6324q6648q7896q87+12q90+60q93+216q98+O(q100) 1440 q + 72 q^{15} + 108 q^{17} + 24 q^{18} + 72 q^{23} - 36 q^{33} + 72 q^{45} + 24 q^{51} - 216 q^{57} + 24 q^{60} - 36 q^{63} - 24 q^{66} - 48 q^{78} - 96 q^{87} + 12 q^{90} + 60 q^{93} + 216 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(1710,[χ])S_{2}^{\mathrm{new}}(1710, [\chi]) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of S2old(1710,[χ])S_{2}^{\mathrm{old}}(1710, [\chi]) into lower level spaces

S2old(1710,[χ]) S_{2}^{\mathrm{old}}(1710, [\chi]) \simeq S2new(855,[χ])S_{2}^{\mathrm{new}}(855, [\chi])2^{\oplus 2}