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Properties

Label 4.17.b
Level $4$
Weight $17$
Character orbit 4.b
Rep. character $\chi_{4}(3,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4.17.b.a 4.b 4.b $1$ $6.493$ \(\Q\) \(\Q(\sqrt{-1}) \) \(256\) \(0\) \(329666\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{8}q^{2}+2^{16}q^{4}+329666q^{5}+2^{24}q^{8}+\cdots\)
4.17.b.b 4.b 4.b $6$ $6.493$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-164\) \(0\) \(-506740\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots\)