Properties

Label 6014.2.a
Level 6014
Weight 2
Character orbit a
Rep. character \(\chi_{6014}(1,\cdot)\)
Character field \(\Q\)
Dimension 239
Newforms 12
Sturm bound 1568
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6014.a (trivial)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(1568\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6014))\).

Total New Old
Modular forms 788 239 549
Cusp forms 781 239 542
Eisenstein series 7 0 7

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

\(2\)\(31\)\(97\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(26\)
\(+\)\(+\)\(-\)\(-\)\(34\)
\(+\)\(-\)\(+\)\(-\)\(38\)
\(+\)\(-\)\(-\)\(+\)\(22\)
\(-\)\(+\)\(+\)\(-\)\(33\)
\(-\)\(+\)\(-\)\(+\)\(27\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(38\)
Plus space\(+\)\(96\)
Minus space\(-\)\(143\)

Trace form

\(239q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 239q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 235q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(239q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 239q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 235q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut +\mathstrut 32q^{15} \) \(\mathstrut +\mathstrut 239q^{16} \) \(\mathstrut +\mathstrut 22q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 233q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 40q^{35} \) \(\mathstrut +\mathstrut 235q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 64q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 24q^{42} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 94q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 271q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 48q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 26q^{53} \) \(\mathstrut +\mathstrut 16q^{54} \) \(\mathstrut +\mathstrut 32q^{55} \) \(\mathstrut +\mathstrut 16q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut +\mathstrut 40q^{59} \) \(\mathstrut +\mathstrut 32q^{60} \) \(\mathstrut -\mathstrut 14q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut +\mathstrut 40q^{63} \) \(\mathstrut +\mathstrut 239q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 32q^{67} \) \(\mathstrut +\mathstrut 22q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 3q^{72} \) \(\mathstrut +\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 60q^{75} \) \(\mathstrut +\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 183q^{81} \) \(\mathstrut -\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 40q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 26q^{90} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 32q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 33q^{98} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 31 97
6014.2.a.a \(1\) \(48.022\) \(\Q\) None \(1\) \(-1\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
6014.2.a.b \(1\) \(48.022\) \(\Q\) None \(1\) \(0\) \(2\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots\)
6014.2.a.c \(2\) \(48.022\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+2\beta q^{3}+q^{4}+(2+\beta )q^{5}-2\beta q^{6}+\cdots\)
6014.2.a.d \(5\) \(48.022\) 5.5.380224.1 None \(5\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
6014.2.a.e \(21\) \(48.022\) None \(21\) \(-10\) \(-10\) \(-11\) \(-\) \(-\) \(+\)
6014.2.a.f \(22\) \(48.022\) None \(-22\) \(0\) \(0\) \(-11\) \(+\) \(-\) \(-\)
6014.2.a.g \(26\) \(48.022\) None \(-26\) \(0\) \(-2\) \(-1\) \(+\) \(+\) \(+\)
6014.2.a.h \(26\) \(48.022\) None \(26\) \(-10\) \(-8\) \(-9\) \(-\) \(+\) \(-\)
6014.2.a.i \(28\) \(48.022\) None \(28\) \(12\) \(10\) \(13\) \(-\) \(+\) \(+\)
6014.2.a.j \(32\) \(48.022\) None \(-32\) \(-2\) \(0\) \(5\) \(+\) \(+\) \(-\)
6014.2.a.k \(37\) \(48.022\) None \(37\) \(9\) \(9\) \(19\) \(-\) \(-\) \(-\)
6014.2.a.l \(38\) \(48.022\) None \(-38\) \(-2\) \(2\) \(3\) \(+\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(97))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(194))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3007))\)\(^{\oplus 2}\)