Properties

Label 17.12.a
Level 17
Weight 12
Character orbit a
Rep. character \(\chi_{17}(1,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 2
Sturm bound 18
Trace bound 1

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 17.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(17))\).

Total New Old
Modular forms 18 14 4
Cusp forms 16 14 2
Eisenstein series 2 0 2

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

\(17\)Dim.
\(+\)\(8\)
\(-\)\(6\)

Trace form

\(14q \) \(\mathstrut +\mathstrut 46q^{2} \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 15370q^{4} \) \(\mathstrut -\mathstrut 4292q^{5} \) \(\mathstrut +\mathstrut 17746q^{6} \) \(\mathstrut +\mathstrut 71852q^{7} \) \(\mathstrut -\mathstrut 173058q^{8} \) \(\mathstrut +\mathstrut 797046q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut 46q^{2} \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 15370q^{4} \) \(\mathstrut -\mathstrut 4292q^{5} \) \(\mathstrut +\mathstrut 17746q^{6} \) \(\mathstrut +\mathstrut 71852q^{7} \) \(\mathstrut -\mathstrut 173058q^{8} \) \(\mathstrut +\mathstrut 797046q^{9} \) \(\mathstrut -\mathstrut 673214q^{10} \) \(\mathstrut -\mathstrut 526804q^{11} \) \(\mathstrut +\mathstrut 1942838q^{12} \) \(\mathstrut +\mathstrut 3758516q^{13} \) \(\mathstrut -\mathstrut 3613816q^{14} \) \(\mathstrut +\mathstrut 912360q^{15} \) \(\mathstrut +\mathstrut 8226226q^{16} \) \(\mathstrut -\mathstrut 2839714q^{17} \) \(\mathstrut +\mathstrut 8686466q^{18} \) \(\mathstrut -\mathstrut 11240288q^{19} \) \(\mathstrut +\mathstrut 44409558q^{20} \) \(\mathstrut +\mathstrut 41986976q^{21} \) \(\mathstrut +\mathstrut 29992986q^{22} \) \(\mathstrut -\mathstrut 76798340q^{23} \) \(\mathstrut -\mathstrut 151613346q^{24} \) \(\mathstrut +\mathstrut 200012338q^{25} \) \(\mathstrut +\mathstrut 3898736q^{26} \) \(\mathstrut +\mathstrut 174116456q^{27} \) \(\mathstrut +\mathstrut 210859792q^{28} \) \(\mathstrut -\mathstrut 258972468q^{29} \) \(\mathstrut -\mathstrut 159989456q^{30} \) \(\mathstrut -\mathstrut 371456620q^{31} \) \(\mathstrut -\mathstrut 74491658q^{32} \) \(\mathstrut -\mathstrut 246365216q^{33} \) \(\mathstrut -\mathstrut 90870848q^{34} \) \(\mathstrut +\mathstrut 687191560q^{35} \) \(\mathstrut -\mathstrut 1184787162q^{36} \) \(\mathstrut -\mathstrut 1048571284q^{37} \) \(\mathstrut +\mathstrut 1499726344q^{38} \) \(\mathstrut +\mathstrut 324651000q^{39} \) \(\mathstrut -\mathstrut 2917454058q^{40} \) \(\mathstrut -\mathstrut 1116864084q^{41} \) \(\mathstrut -\mathstrut 383375592q^{42} \) \(\mathstrut +\mathstrut 1108450592q^{43} \) \(\mathstrut +\mathstrut 3258533550q^{44} \) \(\mathstrut +\mathstrut 2275669548q^{45} \) \(\mathstrut +\mathstrut 4189620772q^{46} \) \(\mathstrut -\mathstrut 5567527520q^{47} \) \(\mathstrut +\mathstrut 4501089838q^{48} \) \(\mathstrut +\mathstrut 10091243646q^{49} \) \(\mathstrut -\mathstrut 2038342106q^{50} \) \(\mathstrut -\mathstrut 1380101004q^{51} \) \(\mathstrut -\mathstrut 3084898544q^{52} \) \(\mathstrut -\mathstrut 487871740q^{53} \) \(\mathstrut -\mathstrut 2810024660q^{54} \) \(\mathstrut -\mathstrut 6299451048q^{55} \) \(\mathstrut -\mathstrut 6178133760q^{56} \) \(\mathstrut -\mathstrut 12155866720q^{57} \) \(\mathstrut +\mathstrut 15131715978q^{58} \) \(\mathstrut +\mathstrut 14529638592q^{59} \) \(\mathstrut +\mathstrut 26595432800q^{60} \) \(\mathstrut -\mathstrut 25675611524q^{61} \) \(\mathstrut -\mathstrut 43307851592q^{62} \) \(\mathstrut +\mathstrut 15170417228q^{63} \) \(\mathstrut -\mathstrut 20861279734q^{64} \) \(\mathstrut +\mathstrut 42496345080q^{65} \) \(\mathstrut +\mathstrut 12924702860q^{66} \) \(\mathstrut +\mathstrut 70124663480q^{67} \) \(\mathstrut -\mathstrut 8723601408q^{68} \) \(\mathstrut -\mathstrut 10532027568q^{69} \) \(\mathstrut -\mathstrut 76100421800q^{70} \) \(\mathstrut -\mathstrut 26116702620q^{71} \) \(\mathstrut -\mathstrut 13980317574q^{72} \) \(\mathstrut -\mathstrut 12455392836q^{73} \) \(\mathstrut -\mathstrut 144742795930q^{74} \) \(\mathstrut +\mathstrut 43318267804q^{75} \) \(\mathstrut +\mathstrut 10119859400q^{76} \) \(\mathstrut +\mathstrut 100619066928q^{77} \) \(\mathstrut -\mathstrut 52631742492q^{78} \) \(\mathstrut -\mathstrut 71714375700q^{79} \) \(\mathstrut +\mathstrut 122289744734q^{80} \) \(\mathstrut -\mathstrut 84963717282q^{81} \) \(\mathstrut +\mathstrut 99296045040q^{82} \) \(\mathstrut +\mathstrut 143601653440q^{83} \) \(\mathstrut +\mathstrut 120528571208q^{84} \) \(\mathstrut -\mathstrut 30492848932q^{85} \) \(\mathstrut +\mathstrut 117618276260q^{86} \) \(\mathstrut -\mathstrut 159891378936q^{87} \) \(\mathstrut -\mathstrut 280242226026q^{88} \) \(\mathstrut +\mathstrut 254963977324q^{89} \) \(\mathstrut -\mathstrut 14714658934q^{90} \) \(\mathstrut -\mathstrut 189744657976q^{91} \) \(\mathstrut -\mathstrut 12966101244q^{92} \) \(\mathstrut +\mathstrut 43609152976q^{93} \) \(\mathstrut +\mathstrut 337819101216q^{94} \) \(\mathstrut -\mathstrut 170603129056q^{95} \) \(\mathstrut +\mathstrut 14769913038q^{96} \) \(\mathstrut +\mathstrut 57157923628q^{97} \) \(\mathstrut +\mathstrut 21076786366q^{98} \) \(\mathstrut -\mathstrut 11267044468q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(17))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.12.a.a \(6\) \(13.062\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-9\) \(-476\) \(-12884\) \(-23436\) \(-\) \(q+(-2+\beta _{1})q^{2}+(-79+\beta _{2})q^{3}+(767+\cdots)q^{4}+\cdots\)
17.12.a.b \(8\) \(13.062\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(55\) \(496\) \(8592\) \(95288\) \(+\) \(q+(7-\beta _{1})q^{2}+(62-\beta _{1}+\beta _{3})q^{3}+(1344+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(17))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(17)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)