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Properties

Label 21.15.h
Level $21$
Weight $15$
Character orbit 21.h
Rep. character $\chi_{21}(2,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $70$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 21.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(21, [\chi])\).

Total New Old
Modular forms 78 78 0
Cusp forms 70 70 0
Eisenstein series 8 8 0

Trace form

\( 70 q - q^{3} + 262142 q^{4} + 160252 q^{6} + 198689 q^{7} + 5356937 q^{9} + O(q^{10}) \) \( 70 q - q^{3} + 262142 q^{4} + 160252 q^{6} + 198689 q^{7} + 5356937 q^{9} - 1376770 q^{10} - 37319924 q^{12} - 218977994 q^{13} - 19887100 q^{15} - 2276798986 q^{16} + 758059564 q^{18} + 99687181 q^{19} - 1389762338 q^{21} - 13015066516 q^{22} - 11129870274 q^{24} + 30803982215 q^{25} + 6436100018 q^{27} + 98180750410 q^{28} + 95263997740 q^{30} - 48692037837 q^{31} - 61357913518 q^{33} + 144108784080 q^{34} + 467272798132 q^{36} - 98310058599 q^{37} - 132042399763 q^{39} - 188369797590 q^{40} - 1366849086694 q^{42} - 531502261402 q^{43} + 1630370006960 q^{45} + 990559436796 q^{46} - 2982177072248 q^{48} + 613414246117 q^{49} + 1017292222392 q^{51} - 4778900443504 q^{52} + 3277090882870 q^{54} + 12906759309460 q^{55} + 3843020918942 q^{57} - 5768047640446 q^{58} + 287760162430 q^{60} - 1010473569302 q^{61} + 599701459015 q^{63} - 36954127890932 q^{64} - 17386249438304 q^{66} + 182728774045 q^{67} + 25667288468760 q^{69} + 4018854775390 q^{70} - 11591877672744 q^{72} + 35586995975109 q^{73} - 21193000615085 q^{75} - 112133693106376 q^{76} - 12515736652808 q^{78} + 49182152390675 q^{79} + 59059522673861 q^{81} + 69977698661332 q^{82} + 116804979691016 q^{84} + 68833645515120 q^{85} - 48065645412358 q^{87} - 26054172075954 q^{88} + 292891695054820 q^{90} - 53139645052639 q^{91} - 14711454927675 q^{93} - 119309499674172 q^{94} - 86053788292318 q^{96} + 349878169048320 q^{97} + 326737546902464 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.15.h.a 21.h 21.h $2$ $26.109$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(2187\) \(0\) \(1461083\) $\mathrm{U}(1)[D_{6}]$ \(q+3^{7}\zeta_{6}q^{3}-2^{14}\zeta_{6}q^{4}+(950035+\cdots)q^{7}+\cdots\)
21.15.h.b 21.h 21.h $68$ $26.109$ None \(0\) \(-2188\) \(0\) \(-1262394\) $\mathrm{SU}(2)[C_{6}]$