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Properties

Label 19.12.a
Level $19$
Weight $12$
Character orbit 19.a
Rep. character $\chi_{19}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $20$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 19.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(19))\).

Total New Old
Modular forms 20 16 4
Cusp forms 18 16 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.

\(19\)Dim
\(+\)\(9\)
\(-\)\(7\)

Trace form

\( 16 q + 78 q^{2} + 506 q^{3} + 18442 q^{4} - 12193 q^{5} + 17746 q^{6} - 21289 q^{7} - 149592 q^{8} + 979300 q^{9} + O(q^{10}) \) \( 16 q + 78 q^{2} + 506 q^{3} + 18442 q^{4} - 12193 q^{5} + 17746 q^{6} - 21289 q^{7} - 149592 q^{8} + 979300 q^{9} + 341688 q^{10} - 1223717 q^{11} + 3492360 q^{12} - 1830142 q^{13} + 838540 q^{14} - 6233230 q^{15} + 17679994 q^{16} + 3402101 q^{17} + 24242358 q^{18} - 4952198 q^{19} - 60129752 q^{20} + 23771926 q^{21} - 32921424 q^{22} - 2365496 q^{23} + 181367310 q^{24} + 158507947 q^{25} - 42768310 q^{26} + 353249516 q^{27} - 319434562 q^{28} - 325489264 q^{29} + 8327804 q^{30} - 118517044 q^{31} + 985456272 q^{32} - 550268602 q^{33} - 157690308 q^{34} - 810439815 q^{35} + 609704716 q^{36} + 98876252 q^{37} - 237705504 q^{38} - 515081352 q^{39} - 3300258804 q^{40} - 67663120 q^{41} - 430356238 q^{42} - 450115753 q^{43} - 1972092304 q^{44} - 1066438561 q^{45} + 6831031716 q^{46} - 5451652275 q^{47} + 146638560 q^{48} + 10657053615 q^{49} + 6593825954 q^{50} + 5342120518 q^{51} - 12611576500 q^{52} + 5011589674 q^{53} - 4624964354 q^{54} - 10374837615 q^{55} + 12333026196 q^{56} - 1203384114 q^{57} + 24172387026 q^{58} + 21182158366 q^{59} - 26944821620 q^{60} - 9408922813 q^{61} + 10328194276 q^{62} - 33056103849 q^{63} + 9781552066 q^{64} + 5512189248 q^{65} + 10593590924 q^{66} + 8921115440 q^{67} - 80270105486 q^{68} - 35689979712 q^{69} - 12237021204 q^{70} + 30429222702 q^{71} + 112867048440 q^{72} + 16481694089 q^{73} - 32312582600 q^{74} + 119964040516 q^{75} - 12677626880 q^{76} + 80851580935 q^{77} - 94915820300 q^{78} - 70851440296 q^{79} - 209151419180 q^{80} - 8024115980 q^{81} - 135136104444 q^{82} - 71467960000 q^{83} + 102342352212 q^{84} + 284747028969 q^{85} - 55245452724 q^{86} - 46540227372 q^{87} - 290089047288 q^{88} + 102444897902 q^{89} - 116755846180 q^{90} + 232285890436 q^{91} + 207214577930 q^{92} - 171735098424 q^{93} + 437130137688 q^{94} - 40660021679 q^{95} + 717917414798 q^{96} - 328812992134 q^{97} - 637037356106 q^{98} - 203910655757 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(19))\) 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
19.12.a.a 19.a 1.a $7$ $14.599$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-9\) \(10\) \(-14307\) \(-2209\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{4})q^{3}+\cdots\)
19.12.a.b 19.a 1.a $9$ $14.599$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(87\) \(496\) \(2114\) \(-19080\) $+$ $\mathrm{SU}(2)$ \(q+(10-\beta _{1})q^{2}+(56-3\beta _{1}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(19))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(19)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)