Properties

Label 14.6.a
Level 14
Weight 6
Character orbit a
Rep. character \(\chi_{14}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 12
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 14.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(14))\).

Total New Old
Modular forms 12 2 10
Cusp forms 8 2 6
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.

\(2\)\(7\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\(2q \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 94q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 322q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 94q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 322q^{9} \) \(\mathstrut -\mathstrut 296q^{10} \) \(\mathstrut -\mathstrut 676q^{11} \) \(\mathstrut +\mathstrut 288q^{12} \) \(\mathstrut +\mathstrut 290q^{13} \) \(\mathstrut -\mathstrut 392q^{14} \) \(\mathstrut +\mathstrut 920q^{15} \) \(\mathstrut +\mathstrut 512q^{16} \) \(\mathstrut -\mathstrut 232q^{17} \) \(\mathstrut -\mathstrut 144q^{18} \) \(\mathstrut +\mathstrut 2902q^{19} \) \(\mathstrut +\mathstrut 1504q^{20} \) \(\mathstrut +\mathstrut 98q^{21} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 2200q^{23} \) \(\mathstrut -\mathstrut 128q^{24} \) \(\mathstrut +\mathstrut 906q^{25} \) \(\mathstrut -\mathstrut 3512q^{26} \) \(\mathstrut -\mathstrut 7236q^{27} \) \(\mathstrut -\mathstrut 1880q^{29} \) \(\mathstrut -\mathstrut 3040q^{30} \) \(\mathstrut +\mathstrut 1484q^{31} \) \(\mathstrut -\mathstrut 6080q^{33} \) \(\mathstrut +\mathstrut 10736q^{34} \) \(\mathstrut +\mathstrut 3626q^{35} \) \(\mathstrut -\mathstrut 5152q^{36} \) \(\mathstrut +\mathstrut 23512q^{37} \) \(\mathstrut +\mathstrut 7848q^{38} \) \(\mathstrut +\mathstrut 3488q^{39} \) \(\mathstrut -\mathstrut 4736q^{40} \) \(\mathstrut -\mathstrut 8352q^{41} \) \(\mathstrut -\mathstrut 3528q^{42} \) \(\mathstrut +\mathstrut 11812q^{43} \) \(\mathstrut -\mathstrut 10816q^{44} \) \(\mathstrut -\mathstrut 13802q^{45} \) \(\mathstrut +\mathstrut 24800q^{46} \) \(\mathstrut -\mathstrut 2124q^{47} \) \(\mathstrut +\mathstrut 4608q^{48} \) \(\mathstrut +\mathstrut 4802q^{49} \) \(\mathstrut -\mathstrut 27824q^{50} \) \(\mathstrut -\mathstrut 4772q^{51} \) \(\mathstrut +\mathstrut 4640q^{52} \) \(\mathstrut -\mathstrut 51876q^{53} \) \(\mathstrut +\mathstrut 1936q^{54} \) \(\mathstrut -\mathstrut 31624q^{55} \) \(\mathstrut -\mathstrut 6272q^{56} \) \(\mathstrut +\mathstrut 24156q^{57} \) \(\mathstrut -\mathstrut 46448q^{58} \) \(\mathstrut +\mathstrut 6646q^{59} \) \(\mathstrut +\mathstrut 14720q^{60} \) \(\mathstrut +\mathstrut 58814q^{61} \) \(\mathstrut +\mathstrut 64912q^{62} \) \(\mathstrut +\mathstrut 1764q^{63} \) \(\mathstrut +\mathstrut 8192q^{64} \) \(\mathstrut +\mathstrut 46116q^{65} \) \(\mathstrut +\mathstrut 2560q^{66} \) \(\mathstrut -\mathstrut 5136q^{67} \) \(\mathstrut -\mathstrut 3712q^{68} \) \(\mathstrut -\mathstrut 26000q^{69} \) \(\mathstrut -\mathstrut 18424q^{70} \) \(\mathstrut +\mathstrut 65144q^{71} \) \(\mathstrut -\mathstrut 2304q^{72} \) \(\mathstrut -\mathstrut 58116q^{73} \) \(\mathstrut -\mathstrut 20592q^{74} \) \(\mathstrut +\mathstrut 15110q^{75} \) \(\mathstrut +\mathstrut 46432q^{76} \) \(\mathstrut +\mathstrut 196q^{77} \) \(\mathstrut -\mathstrut 32768q^{78} \) \(\mathstrut -\mathstrut 21880q^{79} \) \(\mathstrut +\mathstrut 24064q^{80} \) \(\mathstrut +\mathstrut 12638q^{81} \) \(\mathstrut -\mathstrut 83184q^{82} \) \(\mathstrut -\mathstrut 112258q^{83} \) \(\mathstrut +\mathstrut 1568q^{84} \) \(\mathstrut -\mathstrut 110212q^{85} \) \(\mathstrut +\mathstrut 17616q^{86} \) \(\mathstrut -\mathstrut 5308q^{87} \) \(\mathstrut -\mathstrut 256q^{88} \) \(\mathstrut +\mathstrut 18564q^{89} \) \(\mathstrut +\mathstrut 40888q^{90} \) \(\mathstrut +\mathstrut 43022q^{91} \) \(\mathstrut -\mathstrut 35200q^{92} \) \(\mathstrut -\mathstrut 2872q^{93} \) \(\mathstrut +\mathstrut 6000q^{94} \) \(\mathstrut +\mathstrut 63800q^{95} \) \(\mathstrut -\mathstrut 2048q^{96} \) \(\mathstrut +\mathstrut 3672q^{97} \) \(\mathstrut +\mathstrut 108908q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(14))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
14.6.a.a \(1\) \(2.245\) \(\Q\) None \(-4\) \(10\) \(84\) \(49\) \(+\) \(-\) \(q-4q^{2}+10q^{3}+2^{4}q^{4}+84q^{5}-40q^{6}+\cdots\)
14.6.a.b \(1\) \(2.245\) \(\Q\) None \(4\) \(8\) \(10\) \(-49\) \(-\) \(+\) \(q+4q^{2}+8q^{3}+2^{4}q^{4}+10q^{5}+2^{5}q^{6}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)