Properties

Label 38.6.a
Level $38$
Weight $6$
Character orbit 38.a
Rep. character $\chi_{38}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $4$
Sturm bound $30$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 38.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(38))\).

Total New Old
Modular forms 27 7 20
Cusp forms 23 7 16
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(5\)

Trace form

\( 7q + 4q^{2} - 4q^{3} + 112q^{4} + 22q^{5} + 8q^{6} + 194q^{7} + 64q^{8} + 221q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 4q^{3} + 112q^{4} + 22q^{5} + 8q^{6} + 194q^{7} + 64q^{8} + 221q^{9} + 200q^{10} + 320q^{11} - 64q^{12} + 1338q^{13} + 80q^{14} + 1868q^{15} + 1792q^{16} - 1316q^{17} + 628q^{18} - 361q^{19} + 352q^{20} - 2940q^{21} - 1424q^{22} - 3430q^{23} + 128q^{24} - 5899q^{25} - 2144q^{26} + 3464q^{27} + 3104q^{28} - 5566q^{29} - 7792q^{30} - 11164q^{31} + 1024q^{32} - 6800q^{33} + 3080q^{34} - 7788q^{35} + 3536q^{36} + 10038q^{37} - 4332q^{38} + 5046q^{39} + 3200q^{40} + 25722q^{41} + 8632q^{42} - 18208q^{43} + 5120q^{44} + 10810q^{45} + 688q^{46} - 2056q^{47} - 1024q^{48} - 2563q^{49} - 16260q^{50} + 47816q^{51} + 21408q^{52} + 53370q^{53} - 22072q^{54} + 60424q^{55} + 1280q^{56} - 6498q^{57} - 25376q^{58} - 31028q^{59} + 29888q^{60} + 102938q^{61} - 46192q^{62} + 22580q^{63} + 28672q^{64} - 108904q^{65} - 56400q^{66} - 29516q^{67} - 21056q^{68} - 121196q^{69} + 65232q^{70} + 5892q^{71} + 10048q^{72} - 115600q^{73} + 20104q^{74} - 136620q^{75} - 5776q^{76} - 7592q^{77} - 2800q^{78} + 202780q^{79} + 5632q^{80} - 350161q^{81} - 39768q^{82} + 79616q^{83} - 47040q^{84} - 101964q^{85} - 83968q^{86} - 214610q^{87} - 22784q^{88} + 202750q^{89} + 85720q^{90} + 481736q^{91} - 54880q^{92} + 289700q^{93} + 61312q^{94} - 72922q^{95} + 2048q^{96} + 16390q^{97} + 243076q^{98} + 324236q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(38))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
38.6.a.a \(1\) \(6.095\) \(\Q\) None \(-4\) \(-6\) \(31\) \(-27\) \(+\) \(+\) \(q-4q^{2}-6q^{3}+2^{4}q^{4}+31q^{5}+24q^{6}+\cdots\)
38.6.a.b \(1\) \(6.095\) \(\Q\) None \(4\) \(-14\) \(-45\) \(-121\) \(-\) \(-\) \(q+4q^{2}-14q^{3}+2^{4}q^{4}-45q^{5}-56q^{6}+\cdots\)
38.6.a.c \(2\) \(6.095\) \(\Q(\sqrt{1441}) \) None \(-8\) \(3\) \(-45\) \(114\) \(+\) \(-\) \(q-4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots\)
38.6.a.d \(3\) \(6.095\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(13\) \(81\) \(228\) \(-\) \(+\) \(q+4q^{2}+(4+\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(38))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(38)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)