Properties

Label 3700.2.ee
Level 37003700
Weight 22
Character orbit 3700.ee
Rep. character χ3700(13,)\chi_{3700}(13,\cdot)
Character field Q(ζ180)\Q(\zeta_{180})
Dimension 45604560
Sturm bound 11401140

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 3700=225237 3700 = 2^{2} \cdot 5^{2} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3700.ee (of order 180180 and degree 4848)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 925 925
Character field: Q(ζ180)\Q(\zeta_{180})
Sturm bound: 11401140

Dimensions

The following table gives the dimensions of various subspaces of M2(3700,[χ])M_{2}(3700, [\chi]).

Total New Old
Modular forms 27648 4560 23088
Cusp forms 27072 4560 22512
Eisenstein series 576 0 576

Trace form

4560q+6q3+6q1718q25+12q27+6q33+24q35+24q37+30q41228q45+30q53+120q57+120q59+60q61+18q65+78q67180q69120q71+78q97+O(q100) 4560 q + 6 q^{3} + 6 q^{17} - 18 q^{25} + 12 q^{27} + 6 q^{33} + 24 q^{35} + 24 q^{37} + 30 q^{41} - 228 q^{45} + 30 q^{53} + 120 q^{57} + 120 q^{59} + 60 q^{61} + 18 q^{65} + 78 q^{67} - 180 q^{69} - 120 q^{71}+ \cdots - 78 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(3700,[χ])S_{2}^{\mathrm{new}}(3700, [\chi]) into newform subspaces

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

Decomposition of S2old(3700,[χ])S_{2}^{\mathrm{old}}(3700, [\chi]) into lower level spaces

S2old(3700,[χ]) S_{2}^{\mathrm{old}}(3700, [\chi]) \simeq S2new(925,[χ])S_{2}^{\mathrm{new}}(925, [\chi])3^{\oplus 3}\oplusS2new(1850,[χ])S_{2}^{\mathrm{new}}(1850, [\chi])2^{\oplus 2}