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Properties

Label 14.6.c
Level $14$
Weight $6$
Character orbit 14.c
Rep. character $\chi_{14}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
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.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(14, [\chi])\).

Total New Old
Modular forms 24 8 16
Cusp forms 16 8 8
Eisenstein series 8 0 8

Trace form

\( 8 q - 64 q^{4} - 28 q^{5} + 224 q^{6} + 232 q^{7} - 896 q^{9} + O(q^{10}) \) \( 8 q - 64 q^{4} - 28 q^{5} + 224 q^{6} + 232 q^{7} - 896 q^{9} - 448 q^{10} + 232 q^{11} + 3360 q^{13} + 272 q^{14} - 3488 q^{15} - 1024 q^{16} - 2996 q^{17} + 1632 q^{18} + 616 q^{19} + 896 q^{20} + 8692 q^{21} + 2848 q^{22} + 88 q^{23} - 1792 q^{24} - 944 q^{25} - 7840 q^{26} - 17136 q^{27} - 6656 q^{28} - 2368 q^{29} + 9328 q^{30} + 17472 q^{31} + 14924 q^{33} + 3136 q^{34} - 14504 q^{35} + 28672 q^{36} + 3964 q^{37} - 9072 q^{38} - 16328 q^{39} - 7168 q^{40} + 2016 q^{41} - 53856 q^{42} - 41120 q^{43} + 3712 q^{44} + 40544 q^{45} + 21520 q^{46} + 40320 q^{47} + 53768 q^{49} + 93440 q^{50} - 35368 q^{51} - 26880 q^{52} - 38964 q^{53} - 91504 q^{54} - 18704 q^{55} - 14848 q^{56} - 123624 q^{57} + 18080 q^{58} - 37744 q^{59} + 27904 q^{60} + 51660 q^{61} + 96992 q^{62} + 227256 q^{63} + 32768 q^{64} - 31248 q^{65} - 98560 q^{66} + 70640 q^{67} - 47936 q^{68} - 7336 q^{69} - 112784 q^{70} - 200864 q^{71} + 26112 q^{72} + 12068 q^{73} + 57312 q^{74} + 95200 q^{75} - 19712 q^{76} + 4172 q^{77} + 214784 q^{78} - 60792 q^{79} - 7168 q^{80} - 116108 q^{81} - 45024 q^{82} + 47488 q^{83} - 71360 q^{84} - 47336 q^{85} + 46080 q^{86} + 225736 q^{87} - 22784 q^{88} - 47628 q^{89} - 105280 q^{90} - 177552 q^{91} - 2816 q^{92} + 27892 q^{93} + 41328 q^{94} - 157784 q^{95} - 28672 q^{96} - 103936 q^{97} - 50016 q^{98} + 558832 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.6.c.a 14.c 7.c $4$ $2.245$ \(\Q(\sqrt{-3}, \sqrt{79})\) None \(-8\) \(-14\) \(-70\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{2}q^{2}+(-7-\beta _{1}-7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
14.6.c.b 14.c 7.c $4$ $2.245$ \(\Q(\sqrt{-3}, \sqrt{130})\) None \(8\) \(14\) \(42\) \(232\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{2}q^{2}+(7-\beta _{1}+7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)