Properties

Label 3000.2.v
Level 30003000
Weight 22
Character orbit 3000.v
Rep. character χ3000(307,)\chi_{3000}(307,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 384384
Sturm bound 12001200

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 3000=23353 3000 = 2^{3} \cdot 3 \cdot 5^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3000.v (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 40 40
Character field: Q(i)\Q(i)
Sturm bound: 12001200

Dimensions

The following table gives the dimensions of various subspaces of M2(3000,[χ])M_{2}(3000, [\chi]).

Total New Old
Modular forms 1240 384 856
Cusp forms 1160 384 776
Eisenstein series 80 0 80

Trace form

384q+4q620q1616q26+4q36192q4616q51+208q5624q66+48q76384q81+208q86+64q91+96q96+O(q100) 384 q + 4 q^{6} - 20 q^{16} - 16 q^{26} + 4 q^{36} - 192 q^{46} - 16 q^{51} + 208 q^{56} - 24 q^{66} + 48 q^{76} - 384 q^{81} + 208 q^{86} + 64 q^{91} + 96 q^{96}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(3000,[χ])S_{2}^{\mathrm{new}}(3000, [\chi]) into newform subspaces

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

Decomposition of S2old(3000,[χ])S_{2}^{\mathrm{old}}(3000, [\chi]) into lower level spaces

S2old(3000,[χ]) S_{2}^{\mathrm{old}}(3000, [\chi]) \simeq S2new(40,[χ])S_{2}^{\mathrm{new}}(40, [\chi])6^{\oplus 6}\oplusS2new(120,[χ])S_{2}^{\mathrm{new}}(120, [\chi])3^{\oplus 3}\oplusS2new(200,[χ])S_{2}^{\mathrm{new}}(200, [\chi])4^{\oplus 4}\oplusS2new(600,[χ])S_{2}^{\mathrm{new}}(600, [\chi])2^{\oplus 2}\oplusS2new(1000,[χ])S_{2}^{\mathrm{new}}(1000, [\chi])2^{\oplus 2}