Properties

Label 19.6.a
Level $19$
Weight $6$
Character orbit 19.a
Rep. character $\chi_{19}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $10$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 19.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(19))\).

Total New Old
Modular forms 10 8 2
Cusp forms 8 8 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.
\(+\)\(3\)
\(-\)\(5\)

Trace form

\( 8q - 6q^{2} + 2q^{3} + 122q^{4} - 13q^{5} + 106q^{6} - 37q^{7} - 504q^{8} + 712q^{9} + O(q^{10}) \) \( 8q - 6q^{2} + 2q^{3} + 122q^{4} - 13q^{5} + 106q^{6} - 37q^{7} - 504q^{8} + 712q^{9} + 368q^{10} - 401q^{11} - 360q^{12} - 1014q^{13} + 1228q^{14} - 2566q^{15} + 890q^{16} + 2453q^{17} - 4974q^{18} + 722q^{19} - 4568q^{20} + 3286q^{21} + 1648q^{22} + 4768q^{23} + 1902q^{24} + 8911q^{25} + 2138q^{26} - 5092q^{27} - 10674q^{28} + 1520q^{29} + 22316q^{30} + 11324q^{31} - 6144q^{32} - 12994q^{33} - 37036q^{34} - 507q^{35} - 788q^{36} - 844q^{37} + 4332q^{38} - 16320q^{39} + 21900q^{40} - 12712q^{41} - 45574q^{42} + 36739q^{43} + 10976q^{44} + 2003q^{45} - 908q^{46} + 35505q^{47} + 40080q^{48} + 12535q^{49} + 20054q^{50} - 75506q^{51} - 13060q^{52} - 50462q^{53} + 138310q^{54} - 37683q^{55} + 66564q^{56} + 6498q^{57} + 24962q^{58} - 2186q^{59} - 249524q^{60} - 123553q^{61} + 159748q^{62} - 53493q^{63} - 103918q^{64} + 132744q^{65} + 162092q^{66} + 49600q^{67} + 226978q^{68} + 93336q^{69} - 180756q^{70} - 80058q^{71} - 335160q^{72} + 86233q^{73} - 237200q^{74} + 90676q^{75} + 28880q^{76} + 24835q^{77} + 130900q^{78} - 307768q^{79} - 366860q^{80} + 439324q^{81} + 31628q^{82} - 116560q^{83} + 268452q^{84} + 68709q^{85} + 40956q^{86} + 311484q^{87} + 438504q^{88} - 230842q^{89} - 238876q^{90} - 405932q^{91} + 463610q^{92} - 331008q^{93} + 14328q^{94} + 108661q^{95} - 241378q^{96} + 243218q^{97} - 508862q^{98} - 432977q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(19))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19
19.6.a.a \(1\) \(3.047\) \(\Q\) None \(-6\) \(4\) \(54\) \(248\) \(-\) \(q-6q^{2}+4q^{3}+4q^{4}+54q^{5}-24q^{6}+\cdots\)
19.6.a.b \(1\) \(3.047\) \(\Q\) None \(-2\) \(-1\) \(-24\) \(-167\) \(+\) \(q-2q^{2}-q^{3}-28q^{4}-24q^{5}+2q^{6}+\cdots\)
19.6.a.c \(2\) \(3.047\) \(\Q(\sqrt{177}) \) None \(-7\) \(-7\) \(-133\) \(72\) \(+\) \(q+(-3-\beta )q^{2}+(-5+3\beta )q^{3}+(21+\cdots)q^{4}+\cdots\)
19.6.a.d \(4\) \(3.047\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(9\) \(6\) \(90\) \(-190\) \(-\) \(q+(3-\beta _{1}+\beta _{2})q^{2}+(3+3\beta _{2})q^{3}+(23+\cdots)q^{4}+\cdots\)