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Properties

Label 14.8.c
Level $14$
Weight $8$
Character orbit 14.c
Rep. character $\chi_{14}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
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.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(14, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 24 8 16
Eisenstein series 8 0 8

Trace form

\( 8 q - 256 q^{4} + 252 q^{5} - 1792 q^{6} - 1680 q^{7} - 1064 q^{9} + O(q^{10}) \) \( 8 q - 256 q^{4} + 252 q^{5} - 1792 q^{6} - 1680 q^{7} - 1064 q^{9} + 1792 q^{10} - 8256 q^{11} + 24080 q^{13} - 24192 q^{14} + 46576 q^{15} - 16384 q^{16} + 82740 q^{17} - 23040 q^{18} + 43456 q^{19} - 32256 q^{20} - 261884 q^{21} + 55040 q^{22} + 111000 q^{23} + 57344 q^{24} - 107040 q^{25} + 75264 q^{26} - 483840 q^{27} - 53760 q^{28} + 154320 q^{29} + 232576 q^{30} + 236264 q^{31} - 282100 q^{33} - 200704 q^{34} + 129696 q^{35} + 136192 q^{36} + 647980 q^{37} + 309120 q^{38} + 589552 q^{39} + 114688 q^{40} - 700560 q^{41} + 1021440 q^{42} + 651040 q^{43} - 528384 q^{44} - 1794856 q^{45} - 98944 q^{46} - 357000 q^{47} + 367304 q^{49} - 5194752 q^{50} - 2238832 q^{51} - 770560 q^{52} + 43980 q^{53} + 1269632 q^{54} + 10240496 q^{55} + 1032192 q^{56} + 1399800 q^{57} - 2147840 q^{58} - 2502864 q^{59} - 1490432 q^{60} - 2741284 q^{61} + 1532160 q^{62} - 2635920 q^{63} + 2097152 q^{64} - 2810472 q^{65} + 5411840 q^{66} + 3905760 q^{67} + 5295360 q^{68} - 3498712 q^{69} + 9984128 q^{70} + 7749120 q^{71} - 1474560 q^{72} - 2914380 q^{73} - 3773184 q^{74} - 10993136 q^{75} - 5562368 q^{76} - 14111580 q^{77} - 21713920 q^{78} + 17866568 q^{79} + 1032192 q^{80} - 1833716 q^{81} + 15697920 q^{82} - 21245280 q^{83} + 8409856 q^{84} + 24930008 q^{85} + 1683456 q^{86} + 234640 q^{87} - 1761280 q^{88} - 10716300 q^{89} - 19102720 q^{90} - 33681760 q^{91} - 14208000 q^{92} + 21387220 q^{93} + 25452672 q^{94} + 19023576 q^{95} + 3670016 q^{96} + 8250480 q^{97} + 24837120 q^{98} + 59220736 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.8.c.a 14.c 7.c $4$ $4.373$ \(\Q(\sqrt{-3}, \sqrt{2389})\) None \(-16\) \(56\) \(238\) \(168\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-8+8\beta _{1})q^{2}+(28\beta _{1}-\beta _{2})q^{3}+\cdots\)
14.8.c.b 14.c 7.c $4$ $4.373$ \(\Q(\sqrt{-3}, \sqrt{949})\) None \(16\) \(-56\) \(14\) \(-1848\) $\mathrm{SU}(2)[C_{3}]$ \(q+8\beta _{1}q^{2}+(-28+28\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)