Properties

Label 19.8.a
Level $19$
Weight $8$
Character orbit 19.a
Rep. character $\chi_{19}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $13$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 19.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(13\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(19))\).

Total New Old
Modular forms 12 10 2
Cusp forms 10 10 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.

\(19\)Dim
\(+\)\(6\)
\(-\)\(4\)

Trace form

\( 10 q + 6 q^{2} + 26 q^{3} + 394 q^{4} - 3 q^{5} + 322 q^{6} + 859 q^{7} + 2280 q^{8} + 1018 q^{9} + O(q^{10}) \) \( 10 q + 6 q^{2} + 26 q^{3} + 394 q^{4} - 3 q^{5} + 322 q^{6} + 859 q^{7} + 2280 q^{8} + 1018 q^{9} + 1768 q^{10} - 1461 q^{11} + 744 q^{12} + 2370 q^{13} + 6924 q^{14} + 890 q^{15} + 10234 q^{16} + 975 q^{17} - 6258 q^{18} - 13718 q^{19} + 13608 q^{20} - 49166 q^{21} - 108688 q^{22} - 31248 q^{23} - 60978 q^{24} - 77473 q^{25} - 78006 q^{26} + 124508 q^{27} + 129054 q^{28} + 127380 q^{29} - 126436 q^{30} - 39380 q^{31} + 210096 q^{32} + 134066 q^{33} + 537772 q^{34} + 175905 q^{35} - 300692 q^{36} + 811840 q^{37} - 164616 q^{38} + 859224 q^{39} - 293364 q^{40} - 343332 q^{41} - 1024798 q^{42} + 236159 q^{43} - 1690416 q^{44} - 332011 q^{45} + 343556 q^{46} + 88545 q^{47} - 1571712 q^{48} - 606421 q^{49} - 1581846 q^{50} + 975142 q^{51} - 909908 q^{52} + 3303498 q^{53} - 442034 q^{54} - 481635 q^{55} + 2745012 q^{56} - 370386 q^{57} + 2661970 q^{58} - 885954 q^{59} + 1316620 q^{60} + 932281 q^{61} - 2095068 q^{62} - 3233781 q^{63} + 462754 q^{64} + 296448 q^{65} - 111604 q^{66} - 3534352 q^{67} - 848814 q^{68} - 3319512 q^{69} + 6172716 q^{70} + 4767558 q^{71} + 6970200 q^{72} - 4576669 q^{73} + 12391656 q^{74} - 5252924 q^{75} - 2194880 q^{76} - 1691319 q^{77} - 420236 q^{78} + 7345288 q^{79} + 14281620 q^{80} - 13798874 q^{81} - 2233388 q^{82} + 4739088 q^{83} - 16782156 q^{84} - 11785041 q^{85} + 2052972 q^{86} - 15657084 q^{87} - 19763640 q^{88} + 15372558 q^{89} + 5785580 q^{90} + 8899364 q^{91} - 15201174 q^{92} + 18645168 q^{93} - 20440488 q^{94} - 3024819 q^{95} - 7681042 q^{96} - 3884078 q^{97} + 57894318 q^{98} + 36282547 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(19))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 19
19.8.a.a 19.a 1.a $4$ $5.935$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-9\) \(-14\) \(-222\) \(-1246\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{2})q^{3}+\cdots\)
19.8.a.b 19.a 1.a $6$ $5.935$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(15\) \(40\) \(219\) \(2105\) $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(57+\cdots)q^{4}+\cdots\)