Properties

Label 14.4.a
Level 14
Weight 4
Character orbit a
Rep. character \(\chi_{14}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 8
Trace bound 2

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 14.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(14))\).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
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\(+\)\(2\)
Minus space\(-\)\(0\)

Trace form

\( 2q + 6q^{3} + 8q^{4} - 26q^{5} - 20q^{6} + 14q^{9} + O(q^{10}) \) \( 2q + 6q^{3} + 8q^{4} - 26q^{5} - 20q^{6} + 14q^{9} + 4q^{10} + 20q^{11} + 24q^{12} + 74q^{13} + 28q^{14} - 88q^{15} + 32q^{16} - 40q^{17} - 120q^{18} + 82q^{19} - 104q^{20} - 70q^{21} + 152q^{22} - 232q^{23} - 80q^{24} + 90q^{25} + 76q^{26} + 180q^{27} + 136q^{29} + 272q^{30} + 308q^{31} - 320q^{33} - 376q^{34} + 14q^{35} + 56q^{36} - 200q^{37} - 156q^{38} + 32q^{39} + 16q^{40} + 288q^{41} + 84q^{42} - 788q^{43} + 80q^{44} - 242q^{45} - 16q^{46} + 12q^{47} + 96q^{48} + 98q^{49} - 104q^{50} + 820q^{51} + 296q^{52} + 492q^{53} + 40q^{54} - 184q^{55} + 112q^{56} + 636q^{57} - 488q^{58} - 62q^{59} - 352q^{60} + 182q^{61} + 328q^{62} - 420q^{63} + 128q^{64} - 924q^{65} + 256q^{66} - 1200q^{67} - 160q^{68} - 656q^{69} - 364q^{70} + 968q^{71} - 480q^{72} - 612q^{73} + 984q^{74} + 530q^{75} + 328q^{76} + 532q^{77} - 512q^{78} + 1016q^{79} - 416q^{80} + 62q^{81} - 72q^{82} - 694q^{83} - 280q^{84} + 332q^{85} + 72q^{86} + 1628q^{87} + 608q^{88} + 420q^{89} + 1588q^{90} + 266q^{91} - 928q^{92} + 104q^{93} - 72q^{94} - 1144q^{95} - 320q^{96} + 24q^{97} - 2140q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.4.a.a \(1\) \(0.826\) \(\Q\) None \(-2\) \(8\) \(-14\) \(-7\) \(+\) \(+\) \(q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots\)
14.4.a.b \(1\) \(0.826\) \(\Q\) None \(2\) \(-2\) \(-12\) \(7\) \(-\) \(-\) \(q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)