Properties

Label 14.4.a
Level $14$
Weight $4$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
14.4.a.a 14.a 1.a $1$ $0.826$ \(\Q\) None \(-2\) \(8\) \(-14\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots\)
14.4.a.b 14.a 1.a $1$ $0.826$ \(\Q\) None \(2\) \(-2\) \(-12\) \(7\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots\)

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

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