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Properties

Label 21.11.f
Level $21$
Weight $11$
Character orbit 21.f
Rep. character $\chi_{21}(10,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $26$
Newform subspaces $2$
Sturm bound $29$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 21.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(29\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(21, [\chi])\).

Total New Old
Modular forms 58 26 32
Cusp forms 50 26 24
Eisenstein series 8 0 8

Trace form

\( 26 q + 22 q^{2} + 243 q^{3} - 4890 q^{4} - 6666 q^{5} - 1615 q^{7} + 191096 q^{8} + 255879 q^{9} + O(q^{10}) \) \( 26 q + 22 q^{2} + 243 q^{3} - 4890 q^{4} - 6666 q^{5} - 1615 q^{7} + 191096 q^{8} + 255879 q^{9} + 760530 q^{10} + 52606 q^{11} - 497664 q^{12} + 3411718 q^{14} - 662904 q^{15} - 3300842 q^{16} - 4435728 q^{17} - 433026 q^{18} + 10053327 q^{19} - 7835292 q^{21} + 13741388 q^{22} + 10303396 q^{23} - 914166 q^{24} + 27279281 q^{25} - 76245750 q^{26} + 103129398 q^{28} + 157542784 q^{29} + 3337848 q^{30} + 65365653 q^{31} - 199086180 q^{32} - 101992932 q^{33} + 169852254 q^{35} - 192499740 q^{36} - 134529611 q^{37} - 555542466 q^{38} + 20452095 q^{39} - 1192424478 q^{40} + 93659976 q^{42} + 1328006374 q^{43} + 272176308 q^{44} - 131206878 q^{45} - 294377572 q^{46} - 248337618 q^{47} + 917701691 q^{49} + 3880706092 q^{50} - 29011284 q^{51} - 1413923868 q^{52} - 764450384 q^{53} + 252438200 q^{56} + 1300624938 q^{57} - 2329790998 q^{58} + 1714411020 q^{59} + 1754121258 q^{60} - 4349097240 q^{61} + 621923751 q^{63} + 1941212468 q^{64} + 431266782 q^{65} - 5416805340 q^{66} + 1119641755 q^{67} + 3075770052 q^{68} - 2249872158 q^{70} - 5229755540 q^{71} + 1880671284 q^{72} - 729344247 q^{73} - 560752978 q^{74} + 619261929 q^{75} - 15837554132 q^{77} - 13776920964 q^{78} + 3097333621 q^{79} + 33625283808 q^{80} - 5036466357 q^{81} + 25313988960 q^{82} + 11274062760 q^{84} - 24382844256 q^{85} - 9952158274 q^{86} - 4051500606 q^{87} + 25607417134 q^{88} + 17113537596 q^{89} - 4938890367 q^{91} - 75855169320 q^{92} + 3729870909 q^{93} - 13473953448 q^{94} - 19634661690 q^{95} - 24269251266 q^{96} - 31460708912 q^{98} + 2070887796 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.11.f.a 21.f 7.d $12$ $13.343$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(11\) \(-1458\) \(-1287\) \(20090\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+2\beta _{2})q^{2}+(-3^{4}-3^{4}\beta _{2}+\cdots)q^{3}+\cdots\)
21.11.f.b 21.f 7.d $14$ $13.343$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(11\) \(1701\) \(-5379\) \(-21705\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-2\beta _{3})q^{2}+(3^{4}-3^{4}\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)