Properties

Label 128.4.e
Level 128128
Weight 44
Character orbit 128.e
Rep. character χ128(33,)\chi_{128}(33,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 2020
Newform subspaces 22
Sturm bound 6464
Trace bound 33

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Defining parameters

Level: N N == 128=27 128 = 2^{7}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 128.e (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 16 16
Character field: Q(i)\Q(i)
Newform subspaces: 2 2
Sturm bound: 6464
Trace bound: 33
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M4(128,[χ])M_{4}(128, [\chi]).

Total New Old
Modular forms 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

Trace form

20q+4q5+4q138q17104q21+404q298q33+20q37388q45+188q49+756q531820q61984q651160q69+536q77+964q81+24q85+8q97+O(q100) 20 q + 4 q^{5} + 4 q^{13} - 8 q^{17} - 104 q^{21} + 404 q^{29} - 8 q^{33} + 20 q^{37} - 388 q^{45} + 188 q^{49} + 756 q^{53} - 1820 q^{61} - 984 q^{65} - 1160 q^{69} + 536 q^{77} + 964 q^{81} + 24 q^{85}+ \cdots - 8 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(128,[χ])S_{4}^{\mathrm{new}}(128, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
128.4.e.a 128.e 16.e 1010 7.5527.552 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 16.4.e.a 00 2-2 22 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qβ5q3β3q5+(3β1β4)q7+(5β1+)q9+q-\beta _{5}q^{3}-\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(5\beta _{1}+\cdots)q^{9}+\cdots
128.4.e.b 128.e 16.e 1010 7.5527.552 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 16.4.e.a 00 22 22 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q+β5q3β3q5+(3β1+β4)q7+q+\beta _{5}q^{3}-\beta _{3}q^{5}+(-3\beta _{1}+\beta _{4})q^{7}+\cdots

Decomposition of S4old(128,[χ])S_{4}^{\mathrm{old}}(128, [\chi]) into lower level spaces

S4old(128,[χ]) S_{4}^{\mathrm{old}}(128, [\chi]) \simeq S4new(16,[χ])S_{4}^{\mathrm{new}}(16, [\chi])4^{\oplus 4}\oplusS4new(64,[χ])S_{4}^{\mathrm{new}}(64, [\chi])2^{\oplus 2}