Properties

Label 4.17.b
Level 4
Weight 17
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 2
Sturm bound 8
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(4, [\chi])\).

Total New Old
Modular forms 9 9 0
Cusp forms 7 7 0
Eisenstein series 2 2 0

Trace form

\(7q \) \(\mathstrut +\mathstrut 92q^{2} \) \(\mathstrut -\mathstrut 94832q^{4} \) \(\mathstrut -\mathstrut 177074q^{5} \) \(\mathstrut -\mathstrut 1187136q^{6} \) \(\mathstrut -\mathstrut 17051968q^{8} \) \(\mathstrut -\mathstrut 94527801q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 92q^{2} \) \(\mathstrut -\mathstrut 94832q^{4} \) \(\mathstrut -\mathstrut 177074q^{5} \) \(\mathstrut -\mathstrut 1187136q^{6} \) \(\mathstrut -\mathstrut 17051968q^{8} \) \(\mathstrut -\mathstrut 94527801q^{9} \) \(\mathstrut -\mathstrut 57874504q^{10} \) \(\mathstrut +\mathstrut 254142720q^{12} \) \(\mathstrut +\mathstrut 913245134q^{13} \) \(\mathstrut +\mathstrut 1073417856q^{14} \) \(\mathstrut +\mathstrut 4439986432q^{16} \) \(\mathstrut -\mathstrut 8358073586q^{17} \) \(\mathstrut -\mathstrut 11642804388q^{18} \) \(\mathstrut +\mathstrut 26026352416q^{20} \) \(\mathstrut -\mathstrut 27228321792q^{21} \) \(\mathstrut -\mathstrut 138624795840q^{22} \) \(\mathstrut +\mathstrut 403778497536q^{24} \) \(\mathstrut +\mathstrut 227516256981q^{25} \) \(\mathstrut -\mathstrut 608125219400q^{26} \) \(\mathstrut +\mathstrut 1617685224960q^{28} \) \(\mathstrut -\mathstrut 176896760114q^{29} \) \(\mathstrut -\mathstrut 4663806986880q^{30} \) \(\mathstrut +\mathstrut 5762833206272q^{32} \) \(\mathstrut -\mathstrut 767957621760q^{33} \) \(\mathstrut -\mathstrut 8005289437000q^{34} \) \(\mathstrut +\mathstrut 16925800165776q^{36} \) \(\mathstrut +\mathstrut 2413818661454q^{37} \) \(\mathstrut -\mathstrut 20462346561600q^{38} \) \(\mathstrut +\mathstrut 24501932445056q^{40} \) \(\mathstrut -\mathstrut 1327955367026q^{41} \) \(\mathstrut -\mathstrut 20386577111040q^{42} \) \(\mathstrut +\mathstrut 3644055863040q^{44} \) \(\mathstrut -\mathstrut 19975329785394q^{45} \) \(\mathstrut +\mathstrut 5034653652864q^{46} \) \(\mathstrut -\mathstrut 56248898088960q^{48} \) \(\mathstrut +\mathstrut 27705684811399q^{49} \) \(\mathstrut +\mathstrut 118000083874836q^{50} \) \(\mathstrut -\mathstrut 210279285389536q^{52} \) \(\mathstrut +\mathstrut 98705564114254q^{53} \) \(\mathstrut +\mathstrut 366965883430272q^{54} \) \(\mathstrut -\mathstrut 342617610295296q^{56} \) \(\mathstrut -\mathstrut 122486852367360q^{57} \) \(\mathstrut +\mathstrut 321191372059064q^{58} \) \(\mathstrut -\mathstrut 641633781542400q^{60} \) \(\mathstrut -\mathstrut 383495951895346q^{61} \) \(\mathstrut +\mathstrut 619512054551040q^{62} \) \(\mathstrut -\mathstrut 234959061020672q^{64} \) \(\mathstrut +\mathstrut 699899621945372q^{65} \) \(\mathstrut -\mathstrut 54995333852160q^{66} \) \(\mathstrut +\mathstrut 1065376587414304q^{68} \) \(\mathstrut -\mathstrut 265820219762688q^{69} \) \(\mathstrut -\mathstrut 1698017749451520q^{70} \) \(\mathstrut +\mathstrut 2261801294200512q^{72} \) \(\mathstrut +\mathstrut 235441778666894q^{73} \) \(\mathstrut -\mathstrut 2350047094151240q^{74} \) \(\mathstrut +\mathstrut 2768729450169600q^{76} \) \(\mathstrut -\mathstrut 665543599687680q^{77} \) \(\mathstrut -\mathstrut 7024870687386240q^{78} \) \(\mathstrut +\mathstrut 5819231699984896q^{80} \) \(\mathstrut +\mathstrut 1575454067124615q^{81} \) \(\mathstrut -\mathstrut 4270338132400456q^{82} \) \(\mathstrut +\mathstrut 3591637752471552q^{84} \) \(\mathstrut -\mathstrut 5210063079493988q^{85} \) \(\mathstrut +\mathstrut 2096299590206784q^{86} \) \(\mathstrut +\mathstrut 719241463526400q^{88} \) \(\mathstrut +\mathstrut 13469607176070286q^{89} \) \(\mathstrut +\mathstrut 5260731231794616q^{90} \) \(\mathstrut -\mathstrut 9798772065277440q^{92} \) \(\mathstrut -\mathstrut 20365632048291840q^{93} \) \(\mathstrut +\mathstrut 16900683550077696q^{94} \) \(\mathstrut -\mathstrut 32790566117523456q^{96} \) \(\mathstrut +\mathstrut 18568097590556174q^{97} \) \(\mathstrut +\mathstrut 22092056504978012q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.17.b.a \(1\) \(6.493\) \(\Q\) \(\Q(\sqrt{-1}) \) \(256\) \(0\) \(329666\) \(0\) \(q+2^{8}q^{2}+2^{16}q^{4}+329666q^{5}+2^{24}q^{8}+\cdots\)
4.17.b.b \(6\) \(6.493\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-164\) \(0\) \(-506740\) \(0\) \(q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots\)