Properties

Label 704.4.z
Level 704704
Weight 44
Character orbit 704.z
Rep. character χ704(45,)\chi_{704}(45,\cdot)
Character field Q(ζ16)\Q(\zeta_{16})
Dimension 19201920
Sturm bound 384384

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Defining parameters

Level: N N == 704=2611 704 = 2^{6} \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 704.z (of order 1616 and degree 88)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 64 64
Character field: Q(ζ16)\Q(\zeta_{16})
Sturm bound: 384384

Dimensions

The following table gives the dimensions of various subspaces of M4(704,[χ])M_{4}(704, [\chi]).

Total New Old
Modular forms 2320 1920 400
Cusp forms 2288 1920 368
Eisenstein series 32 0 32

Trace form

1920q2000q24+1520q28+4640q30+1760q36880q386320q42+5712q505952q51+3456q544752q58+2752q594896q605856q624128q68++24208q98+O(q100) 1920 q - 2000 q^{24} + 1520 q^{28} + 4640 q^{30} + 1760 q^{36} - 880 q^{38} - 6320 q^{42} + 5712 q^{50} - 5952 q^{51} + 3456 q^{54} - 4752 q^{58} + 2752 q^{59} - 4896 q^{60} - 5856 q^{62} - 4128 q^{68}+ \cdots + 24208 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(704,[χ])S_{4}^{\mathrm{new}}(704, [\chi]) into newform subspaces

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

Decomposition of S4old(704,[χ])S_{4}^{\mathrm{old}}(704, [\chi]) into lower level spaces

S4old(704,[χ]) S_{4}^{\mathrm{old}}(704, [\chi]) \simeq S4new(64,[χ])S_{4}^{\mathrm{new}}(64, [\chi])2^{\oplus 2}