Properties

Label 14.8.a
Level $14$
Weight $8$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $16$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(14))\).

Total New Old
Modular forms 16 4 12
Cusp forms 12 4 8
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
\(+\)\(+\)$+$\(1\)
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(1\)

Trace form

\( 4 q + 16 q^{2} - 78 q^{3} + 256 q^{4} + 174 q^{5} + 688 q^{6} + 1024 q^{8} + 8720 q^{9} + O(q^{10}) \) \( 4 q + 16 q^{2} - 78 q^{3} + 256 q^{4} + 174 q^{5} + 688 q^{6} + 1024 q^{8} + 8720 q^{9} - 5776 q^{10} - 972 q^{11} - 4992 q^{12} - 3734 q^{13} + 5488 q^{14} - 41368 q^{15} + 16384 q^{16} + 516 q^{17} - 2832 q^{18} - 53098 q^{19} + 11136 q^{20} + 74774 q^{21} - 46304 q^{22} - 28152 q^{23} + 44032 q^{24} + 375120 q^{25} - 143728 q^{26} + 1548 q^{27} - 54852 q^{29} + 256832 q^{30} - 31940 q^{31} + 65536 q^{32} - 815984 q^{33} - 35648 q^{34} + 26754 q^{35} + 558080 q^{36} - 465412 q^{37} - 1008496 q^{38} + 230672 q^{39} - 369664 q^{40} + 242460 q^{41} + 148176 q^{42} + 1642172 q^{43} - 62208 q^{44} - 1189082 q^{45} - 19136 q^{46} + 1906020 q^{47} - 319488 q^{48} + 470596 q^{49} + 1039696 q^{50} - 4313924 q^{51} - 238976 q^{52} + 1400616 q^{53} + 3095584 q^{54} + 5313016 q^{55} + 351232 q^{56} - 501468 q^{57} + 970688 q^{58} - 7505418 q^{59} - 2647552 q^{60} + 734830 q^{61} - 4777696 q^{62} - 1609356 q^{63} + 1048576 q^{64} - 2132844 q^{65} - 3368576 q^{66} + 1643016 q^{67} + 33024 q^{68} + 10154464 q^{69} + 2672656 q^{70} - 692616 q^{71} - 181248 q^{72} + 1957104 q^{73} - 290752 q^{74} - 13947610 q^{75} - 3398272 q^{76} - 2012724 q^{77} + 11181568 q^{78} + 5696344 q^{79} + 712704 q^{80} + 8410712 q^{81} + 4193664 q^{82} - 901650 q^{83} + 4785536 q^{84} - 12721028 q^{85} + 12553952 q^{86} + 30574484 q^{87} - 2963456 q^{88} - 10146264 q^{89} - 42033872 q^{90} - 3108266 q^{91} - 1801728 q^{92} - 19258120 q^{93} + 3778272 q^{94} + 23488776 q^{95} + 2818048 q^{96} + 17718564 q^{97} + 1882384 q^{98} - 27165244 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.8.a.a 14.a 1.a $1$ $4.373$ \(\Q\) None \(-8\) \(-82\) \(448\) \(-343\) $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-82q^{3}+2^{6}q^{4}+448q^{5}+\cdots\)
14.8.a.b 14.a 1.a $1$ $4.373$ \(\Q\) None \(8\) \(-66\) \(-400\) \(-343\) $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}-66q^{3}+2^{6}q^{4}-20^{2}q^{5}+\cdots\)
14.8.a.c 14.a 1.a $2$ $4.373$ \(\Q(\sqrt{1969}) \) None \(16\) \(70\) \(126\) \(686\) $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+(35-\beta )q^{3}+2^{6}q^{4}+(63+9\beta )q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)