Properties

Label 17.4.a
Level $17$
Weight $4$
Character orbit 17.a
Rep. character $\chi_{17}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $6$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(17))\).

Total New Old
Modular forms 6 4 2
Cusp forms 4 4 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(17\)Dim.
\(+\)\(3\)
\(-\)\(1\)

Trace form

\( 4 q - 2 q^{2} - 4 q^{3} + 26 q^{4} - 2 q^{5} - 50 q^{6} - 6 q^{7} - 18 q^{8} + 96 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 4 q^{3} + 26 q^{4} - 2 q^{5} - 50 q^{6} - 6 q^{7} - 18 q^{8} + 96 q^{9} - 74 q^{10} - 52 q^{11} + 14 q^{12} - 28 q^{13} + 176 q^{14} + 60 q^{15} + 66 q^{16} - 34 q^{17} - 214 q^{18} + 196 q^{19} - 162 q^{20} + 32 q^{21} + 358 q^{22} + 82 q^{23} - 834 q^{24} - 312 q^{25} + 200 q^{26} - 100 q^{27} + 448 q^{28} - 426 q^{29} + 544 q^{30} + 58 q^{31} - 26 q^{32} - 140 q^{33} - 68 q^{34} - 500 q^{35} + 1350 q^{36} + 298 q^{37} + 376 q^{38} + 732 q^{39} - 298 q^{40} - 636 q^{41} - 1800 q^{42} + 408 q^{43} - 1146 q^{44} - 162 q^{45} - 524 q^{46} + 928 q^{47} + 1342 q^{48} + 172 q^{49} + 814 q^{50} - 204 q^{51} - 832 q^{52} + 620 q^{53} - 860 q^{54} - 68 q^{55} + 96 q^{56} - 1648 q^{57} - 1394 q^{58} + 888 q^{59} + 1280 q^{60} + 26 q^{61} + 1024 q^{62} + 86 q^{63} - 486 q^{64} + 60 q^{65} + 1892 q^{66} + 524 q^{67} - 408 q^{68} + 1056 q^{69} - 1000 q^{70} - 1110 q^{71} - 150 q^{72} + 1200 q^{73} + 1010 q^{74} - 836 q^{75} - 792 q^{76} + 168 q^{77} - 84 q^{78} - 1078 q^{79} - 466 q^{80} - 864 q^{81} + 1384 q^{82} - 1640 q^{83} - 1816 q^{84} + 238 q^{85} - 820 q^{86} + 1188 q^{87} + 1334 q^{88} - 944 q^{89} - 2674 q^{90} + 608 q^{91} + 4836 q^{92} + 2008 q^{93} - 2880 q^{94} + 224 q^{95} + 318 q^{96} - 652 q^{97} + 1534 q^{98} - 3808 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 17
17.4.a.a 17.a 1.a $1$ $1.003$ \(\Q\) None \(-3\) \(-8\) \(6\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b 17.a 1.a $3$ $1.003$ 3.3.2636.1 None \(1\) \(4\) \(-8\) \(22\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)