Properties

Label 14.10.a
Level 14
Weight 10
Character orbit a
Rep. character \(\chi_{14}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 3
Sturm bound 20
Trace bound 2

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 14.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(14))\).

Total New Old
Modular forms 20 4 16
Cusp forms 16 4 12
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\(4q \) \(\mathstrut -\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 150q^{3} \) \(\mathstrut +\mathstrut 1024q^{4} \) \(\mathstrut -\mathstrut 1626q^{5} \) \(\mathstrut +\mathstrut 3040q^{6} \) \(\mathstrut -\mathstrut 8192q^{8} \) \(\mathstrut +\mathstrut 65552q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 150q^{3} \) \(\mathstrut +\mathstrut 1024q^{4} \) \(\mathstrut -\mathstrut 1626q^{5} \) \(\mathstrut +\mathstrut 3040q^{6} \) \(\mathstrut -\mathstrut 8192q^{8} \) \(\mathstrut +\mathstrut 65552q^{9} \) \(\mathstrut +\mathstrut 43424q^{10} \) \(\mathstrut +\mathstrut 39612q^{11} \) \(\mathstrut +\mathstrut 38400q^{12} \) \(\mathstrut -\mathstrut 28766q^{13} \) \(\mathstrut -\mathstrut 76832q^{14} \) \(\mathstrut +\mathstrut 592280q^{15} \) \(\mathstrut +\mathstrut 262144q^{16} \) \(\mathstrut -\mathstrut 885564q^{17} \) \(\mathstrut -\mathstrut 753888q^{18} \) \(\mathstrut +\mathstrut 49442q^{19} \) \(\mathstrut -\mathstrut 416256q^{20} \) \(\mathstrut -\mathstrut 427378q^{21} \) \(\mathstrut +\mathstrut 928576q^{22} \) \(\mathstrut -\mathstrut 2656200q^{23} \) \(\mathstrut +\mathstrut 778240q^{24} \) \(\mathstrut -\mathstrut 1443504q^{25} \) \(\mathstrut -\mathstrut 47776q^{26} \) \(\mathstrut -\mathstrut 3413052q^{27} \) \(\mathstrut +\mathstrut 9137868q^{29} \) \(\mathstrut -\mathstrut 6517120q^{30} \) \(\mathstrut +\mathstrut 3350596q^{31} \) \(\mathstrut -\mathstrut 2097152q^{32} \) \(\mathstrut +\mathstrut 32512912q^{33} \) \(\mathstrut +\mathstrut 13483648q^{34} \) \(\mathstrut -\mathstrut 9205434q^{35} \) \(\mathstrut +\mathstrut 16781312q^{36} \) \(\mathstrut -\mathstrut 36564244q^{37} \) \(\mathstrut -\mathstrut 23716192q^{38} \) \(\mathstrut -\mathstrut 7908112q^{39} \) \(\mathstrut +\mathstrut 11116544q^{40} \) \(\mathstrut +\mathstrut 34564860q^{41} \) \(\mathstrut -\mathstrut 6223392q^{42} \) \(\mathstrut +\mathstrut 13013012q^{43} \) \(\mathstrut +\mathstrut 10140672q^{44} \) \(\mathstrut -\mathstrut 116480402q^{45} \) \(\mathstrut -\mathstrut 36540800q^{46} \) \(\mathstrut +\mathstrut 34924380q^{47} \) \(\mathstrut +\mathstrut 9830400q^{48} \) \(\mathstrut +\mathstrut 23059204q^{49} \) \(\mathstrut -\mathstrut 29933984q^{50} \) \(\mathstrut -\mathstrut 34235276q^{51} \) \(\mathstrut -\mathstrut 7364096q^{52} \) \(\mathstrut -\mathstrut 46913208q^{53} \) \(\mathstrut -\mathstrut 2326208q^{54} \) \(\mathstrut +\mathstrut 36542536q^{55} \) \(\mathstrut -\mathstrut 19668992q^{56} \) \(\mathstrut +\mathstrut 183244164q^{57} \) \(\mathstrut +\mathstrut 31612544q^{58} \) \(\mathstrut -\mathstrut 108522318q^{59} \) \(\mathstrut +\mathstrut 151623680q^{60} \) \(\mathstrut +\mathstrut 76257142q^{61} \) \(\mathstrut +\mathstrut 131969600q^{62} \) \(\mathstrut +\mathstrut 207475212q^{63} \) \(\mathstrut +\mathstrut 67108864q^{64} \) \(\mathstrut -\mathstrut 230680044q^{65} \) \(\mathstrut -\mathstrut 254604032q^{66} \) \(\mathstrut +\mathstrut 580211352q^{67} \) \(\mathstrut -\mathstrut 226704384q^{68} \) \(\mathstrut -\mathstrut 254285600q^{69} \) \(\mathstrut +\mathstrut 105490336q^{70} \) \(\mathstrut +\mathstrut 16036680q^{71} \) \(\mathstrut -\mathstrut 192995328q^{72} \) \(\mathstrut -\mathstrut 142210704q^{73} \) \(\mathstrut +\mathstrut 460406144q^{74} \) \(\mathstrut -\mathstrut 1606313950q^{75} \) \(\mathstrut +\mathstrut 12657152q^{76} \) \(\mathstrut +\mathstrut 120693468q^{77} \) \(\mathstrut +\mathstrut 40164352q^{78} \) \(\mathstrut +\mathstrut 635427112q^{79} \) \(\mathstrut -\mathstrut 106561536q^{80} \) \(\mathstrut +\mathstrut 540236888q^{81} \) \(\mathstrut -\mathstrut 756585216q^{82} \) \(\mathstrut -\mathstrut 134458710q^{83} \) \(\mathstrut -\mathstrut 109408768q^{84} \) \(\mathstrut +\mathstrut 1026034348q^{85} \) \(\mathstrut -\mathstrut 806649664q^{86} \) \(\mathstrut -\mathstrut 1833076660q^{87} \) \(\mathstrut +\mathstrut 237715456q^{88} \) \(\mathstrut +\mathstrut 156632808q^{89} \) \(\mathstrut +\mathstrut 2024135968q^{90} \) \(\mathstrut +\mathstrut 550621330q^{91} \) \(\mathstrut -\mathstrut 679987200q^{92} \) \(\mathstrut +\mathstrut 91836440q^{93} \) \(\mathstrut +\mathstrut 1250460096q^{94} \) \(\mathstrut +\mathstrut 362338680q^{95} \) \(\mathstrut +\mathstrut 199229440q^{96} \) \(\mathstrut -\mathstrut 118654428q^{97} \) \(\mathstrut -\mathstrut 184473632q^{98} \) \(\mathstrut +\mathstrut 2882415692q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.10.a.a \(1\) \(7.211\) \(\Q\) None \(-16\) \(-6\) \(560\) \(-2401\) \(+\) \(+\) \(q-2^{4}q^{2}-6q^{3}+2^{8}q^{4}+560q^{5}+\cdots\)
14.10.a.b \(1\) \(7.211\) \(\Q\) None \(16\) \(170\) \(544\) \(-2401\) \(-\) \(+\) \(q+2^{4}q^{2}+170q^{3}+2^{8}q^{4}+544q^{5}+\cdots\)
14.10.a.c \(2\) \(7.211\) \(\Q(\sqrt{2305}) \) None \(-32\) \(-14\) \(-2730\) \(4802\) \(+\) \(-\) \(q-2^{4}q^{2}+(-7-5\beta )q^{3}+2^{8}q^{4}+(-1365+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)