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Properties

Label 17.12.a
Level $17$
Weight $12$
Character orbit 17.a
Rep. character $\chi_{17}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(17))\) 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
17.12.a.a 17.a 1.a $6$ $13.062$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-9\) \(-476\) \(-12884\) \(-23436\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-79+\beta _{2})q^{3}+(767+\cdots)q^{4}+\cdots\)
17.12.a.b 17.a 1.a $8$ $13.062$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(55\) \(496\) \(8592\) \(95288\) $+$ $\mathrm{SU}(2)$ \(q+(7-\beta _{1})q^{2}+(62-\beta _{1}+\beta _{3})q^{3}+(1344+\cdots)q^{4}+\cdots\)

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

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