Properties

Label 2040.2.h
Level 20402040
Weight 22
Character orbit 2040.h
Rep. character χ2040(1801,)\chi_{2040}(1801,\cdot)
Character field Q\Q
Dimension 3636
Newform subspaces 1010
Sturm bound 864864
Trace bound 1717

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Defining parameters

Level: N N == 2040=233517 2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2040.h (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 17 17
Character field: Q\Q
Newform subspaces: 10 10
Sturm bound: 864864
Trace bound: 1717
Distinguishing TpT_p: 77, 1111, 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(2040,[χ])M_{2}(2040, [\chi]).

Total New Old
Modular forms 448 36 412
Cusp forms 416 36 380
Eisenstein series 32 0 32

Trace form

36q36q98q138q1736q258q3340q4348q4736q49+8q5148q53+8q55+48q59+8q67+16q69+64q77+36q8148q83++8q93+O(q100) 36 q - 36 q^{9} - 8 q^{13} - 8 q^{17} - 36 q^{25} - 8 q^{33} - 40 q^{43} - 48 q^{47} - 36 q^{49} + 8 q^{51} - 48 q^{53} + 8 q^{55} + 48 q^{59} + 8 q^{67} + 16 q^{69} + 64 q^{77} + 36 q^{81} - 48 q^{83}+ \cdots + 8 q^{93}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(2040,[χ])S_{2}^{\mathrm{new}}(2040, [\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}
2040.2.h.a 2040.h 17.b 22 16.28916.289 Q(1)\Q(\sqrt{-1}) None 2040.2.h.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3iq5+4iq7q94iq11+q+i q^{3}-i q^{5}+4 i q^{7}-q^{9}-4 i q^{11}+\cdots
2040.2.h.b 2040.h 17.b 22 16.28916.289 Q(1)\Q(\sqrt{-1}) None 2040.2.h.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3+iq5+4iq7q9+4iq11+q+i q^{3}+i q^{5}+4 i q^{7}-q^{9}+4 i q^{11}+\cdots
2040.2.h.c 2040.h 17.b 22 16.28916.289 Q(1)\Q(\sqrt{-1}) None 2040.2.h.c 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qiq3+iq5+4iq7q92q13+q-i q^{3}+i q^{5}+4 i q^{7}-q^{9}-2 q^{13}+\cdots
2040.2.h.d 2040.h 17.b 22 16.28916.289 Q(1)\Q(\sqrt{-1}) None 2040.2.h.d 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3iq5+2iq7q92q13+q+i q^{3}-i q^{5}+2 i q^{7}-q^{9}-2 q^{13}+\cdots
2040.2.h.e 2040.h 17.b 22 16.28916.289 Q(1)\Q(\sqrt{-1}) None 2040.2.h.e 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3iq5+iq7q95iq11+q+i q^{3}-i q^{5}+i q^{7}-q^{9}-5 i q^{11}+\cdots
2040.2.h.f 2040.h 17.b 22 16.28916.289 Q(1)\Q(\sqrt{-1}) None 2040.2.h.f 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3+iq5+iq7q93iq11+q+i q^{3}+i q^{5}+i q^{7}-q^{9}-3 i q^{11}+\cdots
2040.2.h.g 2040.h 17.b 44 16.28916.289 Q(i,41)\Q(i, \sqrt{41}) None 2040.2.h.g 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β2q3+β2q5+β1q7q9+(β1+)q11+q+\beta _{2}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots
2040.2.h.h 2040.h 17.b 44 16.28916.289 Q(i,17)\Q(i, \sqrt{17}) None 2040.2.h.h 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ2q3+β2q5+(β1β2)q7q9+q-\beta _{2}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+\cdots
2040.2.h.i 2040.h 17.b 66 16.28916.289 6.0.399424.1 None 2040.2.h.i 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ2q3+β2q5+(2β2+β3)q7q9+q-\beta _{2}q^{3}+\beta _{2}q^{5}+(2\beta _{2}+\beta _{3})q^{7}-q^{9}+\cdots
2040.2.h.j 2040.h 17.b 1010 16.28916.289 10.0.\cdots.1 None 2040.2.h.j 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ4q3β4q5+(β4+β8)q7q9+q-\beta _{4}q^{3}-\beta _{4}q^{5}+(\beta _{4}+\beta _{8})q^{7}-q^{9}+\cdots

Decomposition of S2old(2040,[χ])S_{2}^{\mathrm{old}}(2040, [\chi]) into lower level spaces