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

Related objects

Downloads

Learn more about

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

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

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

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