Properties

Label 14.2.a
Level 14
Weight 2
Character orbit a
Rep. character \(\chi_{14}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 4
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 14.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(14))\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

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.
\(+\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + q^{7} - q^{8} + q^{9} - 2q^{12} - 4q^{13} - q^{14} + q^{16} + 6q^{17} - q^{18} + 2q^{19} - 2q^{21} + 2q^{24} - 5q^{25} + 4q^{26} + 4q^{27} + q^{28} - 6q^{29} - 4q^{31} - q^{32} - 6q^{34} + q^{36} + 2q^{37} - 2q^{38} + 8q^{39} + 6q^{41} + 2q^{42} + 8q^{43} - 12q^{47} - 2q^{48} + q^{49} + 5q^{50} - 12q^{51} - 4q^{52} + 6q^{53} - 4q^{54} - q^{56} - 4q^{57} + 6q^{58} - 6q^{59} + 8q^{61} + 4q^{62} + q^{63} + q^{64} - 4q^{67} + 6q^{68} - q^{72} + 2q^{73} - 2q^{74} + 10q^{75} + 2q^{76} - 8q^{78} + 8q^{79} - 11q^{81} - 6q^{82} - 6q^{83} - 2q^{84} - 8q^{86} + 12q^{87} - 6q^{89} - 4q^{91} + 8q^{93} + 12q^{94} + 2q^{96} - 10q^{97} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.2.a.a \(1\) \(0.112\) \(\Q\) None \(-1\) \(-2\) \(0\) \(1\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)