Properties

Label 14.14.c
Level $14$
Weight $14$
Character orbit 14.c
Rep. character $\chi_{14}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $2$
Sturm bound $28$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 14 \)
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: \(28\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 56 16 40
Cusp forms 48 16 32
Eisenstein series 8 0 8

Trace form

\( 16q - 32768q^{4} - 62608q^{5} + 46592q^{6} - 382088q^{7} - 3383912q^{9} + O(q^{10}) \) \( 16q - 32768q^{4} - 62608q^{5} + 46592q^{6} - 382088q^{7} - 3383912q^{9} - 4236288q^{10} - 9735704q^{11} + 55245680q^{13} + 50511104q^{14} - 225762128q^{15} - 134217728q^{16} - 173276096q^{17} - 293349888q^{18} - 639112600q^{19} + 512884736q^{20} - 183034712q^{21} - 987919872q^{22} + 224305888q^{23} - 95420416q^{24} - 1799862224q^{25} - 1675803136q^{26} - 13674585456q^{27} + 1788903424q^{28} + 11874828752q^{29} - 1535497472q^{30} + 7620869816q^{31} + 8347025624q^{33} + 20145914880q^{34} + 37241892856q^{35} + 27721007104q^{36} - 22905358216q^{37} - 13292735232q^{38} + 12213789640q^{39} - 17351835648q^{40} + 200030490576q^{41} + 41592359424q^{42} - 200631743680q^{43} - 39877443584q^{44} - 224768920936q^{45} + 22282358016q^{46} - 84492403800q^{47} + 90125959504q^{49} - 109545902080q^{50} - 226281443320q^{51} - 113143152640q^{52} + 237123627816q^{53} + 228393530624q^{54} + 876549420096q^{55} + 40531656704q^{56} - 1935534418224q^{57} - 784848668160q^{58} - 1060437579040q^{59} + 462360838144q^{60} - 302092281064q^{61} + 589655209472q^{62} + 4198235629896q^{63} + 1099511627776q^{64} - 2789615117688q^{65} - 2695993323520q^{66} + 1651685797520q^{67} - 709738889216q^{68} + 9547459848416q^{69} + 4454335286016q^{70} - 2636562006944q^{71} - 1201561141248q^{72} - 6459088113352q^{73} - 960899357184q^{74} - 3701297994800q^{75} + 5235610419200q^{76} + 13324767549632q^{77} - 7591038447616q^{78} - 7522339758880q^{79} - 1050387939328q^{80} + 2466709187776q^{81} - 872746581504q^{82} + 3647678607328q^{83} + 143615524864q^{84} - 16115442141936q^{85} - 560528154624q^{86} - 14980266985544q^{87} + 2023259897856q^{88} + 1552477239432q^{89} + 1899518028800q^{90} + 4632739903568q^{91} - 1837513834496q^{92} - 17584118617448q^{93} - 5005439894784q^{94} + 15813845642416q^{95} - 390842023936q^{96} + 9790396414064q^{97} - 2608265565696q^{98} - 1131414590864q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.14.c.a \(8\) \(15.012\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-256\) \(-182\) \(-64400\) \(-113736\) \(q+(-2^{6}-2^{6}\beta _{1})q^{2}+(45\beta _{1}+\beta _{4})q^{3}+\cdots\)
14.14.c.b \(8\) \(15.012\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(256\) \(182\) \(1792\) \(-268352\) \(q+(2^{6}+2^{6}\beta _{1})q^{2}+(-46\beta _{1}-\beta _{2})q^{3}+\cdots\)

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

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