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Properties

Label 14.6.a
Level $14$
Weight $6$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $12$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(14))\).

Total New Old
Modular forms 12 2 10
Cusp forms 8 2 6
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\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2 q + 18 q^{3} + 32 q^{4} + 94 q^{5} - 8 q^{6} - 322 q^{9} + O(q^{10}) \) \( 2 q + 18 q^{3} + 32 q^{4} + 94 q^{5} - 8 q^{6} - 322 q^{9} - 296 q^{10} - 676 q^{11} + 288 q^{12} + 290 q^{13} - 392 q^{14} + 920 q^{15} + 512 q^{16} - 232 q^{17} - 144 q^{18} + 2902 q^{19} + 1504 q^{20} + 98 q^{21} - 16 q^{22} - 2200 q^{23} - 128 q^{24} + 906 q^{25} - 3512 q^{26} - 7236 q^{27} - 1880 q^{29} - 3040 q^{30} + 1484 q^{31} - 6080 q^{33} + 10736 q^{34} + 3626 q^{35} - 5152 q^{36} + 23512 q^{37} + 7848 q^{38} + 3488 q^{39} - 4736 q^{40} - 8352 q^{41} - 3528 q^{42} + 11812 q^{43} - 10816 q^{44} - 13802 q^{45} + 24800 q^{46} - 2124 q^{47} + 4608 q^{48} + 4802 q^{49} - 27824 q^{50} - 4772 q^{51} + 4640 q^{52} - 51876 q^{53} + 1936 q^{54} - 31624 q^{55} - 6272 q^{56} + 24156 q^{57} - 46448 q^{58} + 6646 q^{59} + 14720 q^{60} + 58814 q^{61} + 64912 q^{62} + 1764 q^{63} + 8192 q^{64} + 46116 q^{65} + 2560 q^{66} - 5136 q^{67} - 3712 q^{68} - 26000 q^{69} - 18424 q^{70} + 65144 q^{71} - 2304 q^{72} - 58116 q^{73} - 20592 q^{74} + 15110 q^{75} + 46432 q^{76} + 196 q^{77} - 32768 q^{78} - 21880 q^{79} + 24064 q^{80} + 12638 q^{81} - 83184 q^{82} - 112258 q^{83} + 1568 q^{84} - 110212 q^{85} + 17616 q^{86} - 5308 q^{87} - 256 q^{88} + 18564 q^{89} + 40888 q^{90} + 43022 q^{91} - 35200 q^{92} - 2872 q^{93} + 6000 q^{94} + 63800 q^{95} - 2048 q^{96} + 3672 q^{97} + 108908 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.6.a.a 14.a 1.a $1$ $2.245$ \(\Q\) None \(-4\) \(10\) \(84\) \(49\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+10q^{3}+2^{4}q^{4}+84q^{5}-40q^{6}+\cdots\)
14.6.a.b 14.a 1.a $1$ $2.245$ \(\Q\) None \(4\) \(8\) \(10\) \(-49\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{3}+2^{4}q^{4}+10q^{5}+2^{5}q^{6}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)