Properties

Label 14.8.a
Level 14
Weight 8
Character orbit a
Rep. character \(\chi_{14}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 3
Sturm bound 16
Trace bound 2

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 14.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(14))\).

Total New Old
Modular forms 16 4 12
Cusp forms 12 4 8
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.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(1\)

Trace form

\(4q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 78q^{3} \) \(\mathstrut +\mathstrut 256q^{4} \) \(\mathstrut +\mathstrut 174q^{5} \) \(\mathstrut +\mathstrut 688q^{6} \) \(\mathstrut +\mathstrut 1024q^{8} \) \(\mathstrut +\mathstrut 8720q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 78q^{3} \) \(\mathstrut +\mathstrut 256q^{4} \) \(\mathstrut +\mathstrut 174q^{5} \) \(\mathstrut +\mathstrut 688q^{6} \) \(\mathstrut +\mathstrut 1024q^{8} \) \(\mathstrut +\mathstrut 8720q^{9} \) \(\mathstrut -\mathstrut 5776q^{10} \) \(\mathstrut -\mathstrut 972q^{11} \) \(\mathstrut -\mathstrut 4992q^{12} \) \(\mathstrut -\mathstrut 3734q^{13} \) \(\mathstrut +\mathstrut 5488q^{14} \) \(\mathstrut -\mathstrut 41368q^{15} \) \(\mathstrut +\mathstrut 16384q^{16} \) \(\mathstrut +\mathstrut 516q^{17} \) \(\mathstrut -\mathstrut 2832q^{18} \) \(\mathstrut -\mathstrut 53098q^{19} \) \(\mathstrut +\mathstrut 11136q^{20} \) \(\mathstrut +\mathstrut 74774q^{21} \) \(\mathstrut -\mathstrut 46304q^{22} \) \(\mathstrut -\mathstrut 28152q^{23} \) \(\mathstrut +\mathstrut 44032q^{24} \) \(\mathstrut +\mathstrut 375120q^{25} \) \(\mathstrut -\mathstrut 143728q^{26} \) \(\mathstrut +\mathstrut 1548q^{27} \) \(\mathstrut -\mathstrut 54852q^{29} \) \(\mathstrut +\mathstrut 256832q^{30} \) \(\mathstrut -\mathstrut 31940q^{31} \) \(\mathstrut +\mathstrut 65536q^{32} \) \(\mathstrut -\mathstrut 815984q^{33} \) \(\mathstrut -\mathstrut 35648q^{34} \) \(\mathstrut +\mathstrut 26754q^{35} \) \(\mathstrut +\mathstrut 558080q^{36} \) \(\mathstrut -\mathstrut 465412q^{37} \) \(\mathstrut -\mathstrut 1008496q^{38} \) \(\mathstrut +\mathstrut 230672q^{39} \) \(\mathstrut -\mathstrut 369664q^{40} \) \(\mathstrut +\mathstrut 242460q^{41} \) \(\mathstrut +\mathstrut 148176q^{42} \) \(\mathstrut +\mathstrut 1642172q^{43} \) \(\mathstrut -\mathstrut 62208q^{44} \) \(\mathstrut -\mathstrut 1189082q^{45} \) \(\mathstrut -\mathstrut 19136q^{46} \) \(\mathstrut +\mathstrut 1906020q^{47} \) \(\mathstrut -\mathstrut 319488q^{48} \) \(\mathstrut +\mathstrut 470596q^{49} \) \(\mathstrut +\mathstrut 1039696q^{50} \) \(\mathstrut -\mathstrut 4313924q^{51} \) \(\mathstrut -\mathstrut 238976q^{52} \) \(\mathstrut +\mathstrut 1400616q^{53} \) \(\mathstrut +\mathstrut 3095584q^{54} \) \(\mathstrut +\mathstrut 5313016q^{55} \) \(\mathstrut +\mathstrut 351232q^{56} \) \(\mathstrut -\mathstrut 501468q^{57} \) \(\mathstrut +\mathstrut 970688q^{58} \) \(\mathstrut -\mathstrut 7505418q^{59} \) \(\mathstrut -\mathstrut 2647552q^{60} \) \(\mathstrut +\mathstrut 734830q^{61} \) \(\mathstrut -\mathstrut 4777696q^{62} \) \(\mathstrut -\mathstrut 1609356q^{63} \) \(\mathstrut +\mathstrut 1048576q^{64} \) \(\mathstrut -\mathstrut 2132844q^{65} \) \(\mathstrut -\mathstrut 3368576q^{66} \) \(\mathstrut +\mathstrut 1643016q^{67} \) \(\mathstrut +\mathstrut 33024q^{68} \) \(\mathstrut +\mathstrut 10154464q^{69} \) \(\mathstrut +\mathstrut 2672656q^{70} \) \(\mathstrut -\mathstrut 692616q^{71} \) \(\mathstrut -\mathstrut 181248q^{72} \) \(\mathstrut +\mathstrut 1957104q^{73} \) \(\mathstrut -\mathstrut 290752q^{74} \) \(\mathstrut -\mathstrut 13947610q^{75} \) \(\mathstrut -\mathstrut 3398272q^{76} \) \(\mathstrut -\mathstrut 2012724q^{77} \) \(\mathstrut +\mathstrut 11181568q^{78} \) \(\mathstrut +\mathstrut 5696344q^{79} \) \(\mathstrut +\mathstrut 712704q^{80} \) \(\mathstrut +\mathstrut 8410712q^{81} \) \(\mathstrut +\mathstrut 4193664q^{82} \) \(\mathstrut -\mathstrut 901650q^{83} \) \(\mathstrut +\mathstrut 4785536q^{84} \) \(\mathstrut -\mathstrut 12721028q^{85} \) \(\mathstrut +\mathstrut 12553952q^{86} \) \(\mathstrut +\mathstrut 30574484q^{87} \) \(\mathstrut -\mathstrut 2963456q^{88} \) \(\mathstrut -\mathstrut 10146264q^{89} \) \(\mathstrut -\mathstrut 42033872q^{90} \) \(\mathstrut -\mathstrut 3108266q^{91} \) \(\mathstrut -\mathstrut 1801728q^{92} \) \(\mathstrut -\mathstrut 19258120q^{93} \) \(\mathstrut +\mathstrut 3778272q^{94} \) \(\mathstrut +\mathstrut 23488776q^{95} \) \(\mathstrut +\mathstrut 2818048q^{96} \) \(\mathstrut +\mathstrut 17718564q^{97} \) \(\mathstrut +\mathstrut 1882384q^{98} \) \(\mathstrut -\mathstrut 27165244q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.8.a.a \(1\) \(4.373\) \(\Q\) None \(-8\) \(-82\) \(448\) \(-343\) \(+\) \(+\) \(q-8q^{2}-82q^{3}+2^{6}q^{4}+448q^{5}+\cdots\)
14.8.a.b \(1\) \(4.373\) \(\Q\) None \(8\) \(-66\) \(-400\) \(-343\) \(-\) \(+\) \(q+8q^{2}-66q^{3}+2^{6}q^{4}-20^{2}q^{5}+\cdots\)
14.8.a.c \(2\) \(4.373\) \(\Q(\sqrt{1969}) \) None \(16\) \(70\) \(126\) \(686\) \(-\) \(-\) \(q+8q^{2}+(35-\beta )q^{3}+2^{6}q^{4}+(63+9\beta )q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)