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Properties

Label 19.10.a
Level $19$
Weight $10$
Character orbit 19.a
Rep. character $\chi_{19}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 19.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(19))\).

Total New Old
Modular forms 16 14 2
Cusp forms 14 14 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
\(+\)\(6\)
\(-\)\(8\)

Trace form

\( 14 q - 18 q^{2} - 148 q^{3} + 4010 q^{4} + 282 q^{5} - 4142 q^{6} - 3048 q^{7} - 12600 q^{8} + 120340 q^{9} + O(q^{10}) \) \( 14 q - 18 q^{2} - 148 q^{3} + 4010 q^{4} + 282 q^{5} - 4142 q^{6} - 3048 q^{7} - 12600 q^{8} + 120340 q^{9} + 19288 q^{10} + 103506 q^{11} - 111048 q^{12} - 82456 q^{13} - 393732 q^{14} + 130904 q^{15} + 1604282 q^{16} + 295380 q^{17} - 850698 q^{18} + 260642 q^{19} + 1640232 q^{20} - 2888000 q^{21} + 2466944 q^{22} - 2343102 q^{23} - 1921554 q^{24} + 7332216 q^{25} + 3572826 q^{26} - 11407192 q^{27} + 9077678 q^{28} - 2632332 q^{29} - 22890244 q^{30} - 12588132 q^{31} - 21162528 q^{32} + 31551428 q^{33} - 22374980 q^{34} + 11467278 q^{35} + 19825948 q^{36} + 8798496 q^{37} + 6255408 q^{38} - 26244450 q^{39} + 35716620 q^{40} + 9917640 q^{41} + 8826002 q^{42} - 38494406 q^{43} + 120967968 q^{44} + 47802638 q^{45} - 151614364 q^{46} - 73866414 q^{47} + 141647088 q^{48} + 132775106 q^{49} + 191811234 q^{50} - 25081076 q^{51} - 111826308 q^{52} - 124055520 q^{53} - 184629938 q^{54} + 260022402 q^{55} - 699193500 q^{56} + 21112002 q^{57} - 385408766 q^{58} + 13405548 q^{59} + 375959116 q^{60} + 372498678 q^{61} + 113577396 q^{62} + 455976042 q^{63} + 348050162 q^{64} - 168041796 q^{65} - 1140846148 q^{66} - 14342432 q^{67} + 520247394 q^{68} + 483883740 q^{69} + 176441244 q^{70} + 9161880 q^{71} - 2128825752 q^{72} - 551284400 q^{73} + 1054592664 q^{74} - 527358704 q^{75} + 166810880 q^{76} - 1178671734 q^{77} + 1235054212 q^{78} + 657938172 q^{79} + 604352820 q^{80} + 712299382 q^{81} + 2866982068 q^{82} + 472925340 q^{83} - 3162362940 q^{84} + 365700774 q^{85} - 105075492 q^{86} + 116369070 q^{87} + 194158248 q^{88} - 2555324040 q^{89} + 1864409564 q^{90} - 178213392 q^{91} + 1668121530 q^{92} + 2005379004 q^{93} - 3623996616 q^{94} + 978189426 q^{95} + 1619378942 q^{96} - 777943680 q^{97} - 67154058 q^{98} - 637221746 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(19))\) 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
19.10.a.a 19.a 1.a $6$ $9.786$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-33\) \(-155\) \(-3612\) \(4085\) $+$ $\mathrm{SU}(2)$ \(q+(-6+\beta _{1})q^{2}+(-26+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
19.10.a.b 19.a 1.a $8$ $9.786$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(15\) \(7\) \(3894\) \(-7133\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(1+\beta _{1}-\beta _{3})q^{3}+(331+\cdots)q^{4}+\cdots\)