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Properties

Label 17.6.a
Level $17$
Weight $6$
Character orbit 17.a
Rep. character $\chi_{17}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $9$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(9\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(17))\).

Total New Old
Modular forms 8 6 2
Cusp forms 6 6 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
\(+\)\(2\)
\(-\)\(4\)

Trace form

\( 6 q - 2 q^{2} + 20 q^{3} + 42 q^{4} - 8 q^{5} + 106 q^{6} + 116 q^{7} - 66 q^{8} + 6 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{2} + 20 q^{3} + 42 q^{4} - 8 q^{5} + 106 q^{6} + 116 q^{7} - 66 q^{8} + 6 q^{9} - 262 q^{10} - 100 q^{11} - 586 q^{12} + 412 q^{13} - 472 q^{14} - 1176 q^{15} - 1166 q^{16} + 578 q^{17} + 1682 q^{18} + 1040 q^{19} + 438 q^{20} + 752 q^{21} - 2702 q^{22} + 4660 q^{23} + 2958 q^{24} + 7474 q^{25} - 5584 q^{26} + 3608 q^{27} + 1424 q^{28} - 4824 q^{29} - 9488 q^{30} - 1956 q^{31} - 4394 q^{32} - 9512 q^{33} + 2312 q^{34} + 8056 q^{35} - 20682 q^{36} - 672 q^{37} - 13352 q^{38} - 19896 q^{39} + 14678 q^{40} + 45108 q^{41} + 49464 q^{42} - 16576 q^{43} + 25758 q^{44} - 24264 q^{45} + 32900 q^{46} - 32720 q^{47} - 42434 q^{48} + 3718 q^{49} + 5110 q^{50} + 10404 q^{51} + 79968 q^{52} - 100180 q^{53} + 17260 q^{54} - 7688 q^{55} - 94032 q^{56} - 880 q^{57} + 162706 q^{58} + 61824 q^{59} - 88480 q^{60} + 62304 q^{61} - 46856 q^{62} + 91316 q^{63} - 76918 q^{64} - 133296 q^{65} - 77764 q^{66} - 26840 q^{67} + 27744 q^{68} + 91680 q^{69} - 257352 q^{70} + 107100 q^{71} - 72822 q^{72} - 145332 q^{73} + 69230 q^{74} + 351820 q^{75} + 248024 q^{76} - 200016 q^{77} + 262836 q^{78} - 51676 q^{79} + 205502 q^{80} - 144354 q^{81} - 269840 q^{82} - 5600 q^{83} - 111640 q^{84} + 48552 q^{85} + 223460 q^{86} - 255768 q^{87} + 142838 q^{88} - 112532 q^{89} - 300814 q^{90} + 264328 q^{91} + 386628 q^{92} + 279952 q^{93} - 329376 q^{94} + 257072 q^{95} - 186978 q^{96} + 150564 q^{97} - 241298 q^{98} - 310948 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(17))\) 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
17.6.a.a 17.a 1.a $1$ $2.727$ \(\Q\) None \(-6\) \(10\) \(-72\) \(-196\) $+$ $\mathrm{SU}(2)$ \(q-6q^{2}+10q^{3}+4q^{4}-72q^{5}-60q^{6}+\cdots\)
17.6.a.b 17.a 1.a $1$ $2.727$ \(\Q\) None \(1\) \(-18\) \(-16\) \(28\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-18q^{3}-31q^{4}-2^{4}q^{5}-18q^{6}+\cdots\)
17.6.a.c 17.a 1.a $4$ $2.727$ 4.4.5416116.1 None \(3\) \(28\) \(80\) \(284\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(7+\beta _{1}-\beta _{3})q^{3}+(18+\cdots)q^{4}+\cdots\)