Properties

Label 14.10.a
Level $14$
Weight $10$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
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: \(\Q\)
Newform subspaces: \( 3 \)
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

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

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(14))\) into newform subspaces

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

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