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Properties

Label 14.11.d
Level $14$
Weight $11$
Character orbit 14.d
Rep. character $\chi_{14}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 14.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(14, [\chi])\).

Total New Old
Modular forms 44 12 32
Cusp forms 36 12 24
Eisenstein series 8 0 8

Trace form

\( 12 q + 486 q^{3} - 3072 q^{4} - 6666 q^{5} + 30576 q^{7} - 45528 q^{9} + O(q^{10}) \) \( 12 q + 486 q^{3} - 3072 q^{4} - 6666 q^{5} + 30576 q^{7} - 45528 q^{9} + 130944 q^{10} - 111210 q^{11} - 248832 q^{12} - 38976 q^{14} + 1065684 q^{15} - 1572864 q^{16} + 1439502 q^{17} + 715392 q^{18} - 452814 q^{19} - 2940462 q^{21} - 1922688 q^{22} + 853074 q^{23} - 9338880 q^{24} + 16905804 q^{25} - 8671872 q^{26} + 4064256 q^{28} + 60157248 q^{29} - 37409472 q^{30} + 87231186 q^{31} - 303597198 q^{33} + 153795138 q^{35} + 46620672 q^{36} - 7666506 q^{37} - 21703872 q^{38} - 71628084 q^{39} - 67043328 q^{40} + 129553536 q^{42} + 1066803336 q^{43} - 56939520 q^{44} - 948611736 q^{45} - 168245184 q^{46} - 985909398 q^{47} + 456183924 q^{49} + 1764094464 q^{50} - 319431390 q^{51} - 538871808 q^{52} - 600022554 q^{53} - 402417216 q^{54} - 243597312 q^{56} + 3357095652 q^{57} - 294598272 q^{58} - 2101762050 q^{59} - 272815104 q^{60} - 2201391150 q^{61} + 2691345552 q^{63} + 1610612736 q^{64} + 1536128076 q^{65} + 728780544 q^{66} - 1590058326 q^{67} - 737025024 q^{68} - 3745457856 q^{70} - 7739561160 q^{71} + 366280704 q^{72} + 2008593834 q^{73} + 1042308096 q^{74} + 12301086492 q^{75} + 464655282 q^{77} - 8450806272 q^{78} + 2310562242 q^{79} + 1747451904 q^{80} + 7562341422 q^{81} + 9636272256 q^{82} - 7405267968 q^{84} - 39581743596 q^{85} - 4924086912 q^{86} + 24592790952 q^{87} + 492208128 q^{88} + 2541648690 q^{89} - 4866473640 q^{91} - 873547776 q^{92} - 7836264270 q^{93} + 28852652352 q^{94} + 29024266590 q^{95} + 4781506560 q^{96} - 11553118080 q^{98} - 13213951200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.11.d.a 14.d 7.d $12$ $8.895$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(486\) \(-6666\) \(30576\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(54+3^{3}\beta _{1}-2\beta _{2}-2\beta _{3}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)