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Properties

Label 11.14.a
Level $11$
Weight $14$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $14$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(11))\).

Total New Old
Modular forms 14 12 2
Cusp forms 12 12 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(11\)Dim
\(+\)\(5\)
\(-\)\(7\)

Trace form

\( 12 q - 64 q^{2} + 859 q^{3} + 44692 q^{4} + 52235 q^{5} - 269570 q^{6} - 403306 q^{7} - 835572 q^{8} + 6590309 q^{9} + O(q^{10}) \) \( 12 q - 64 q^{2} + 859 q^{3} + 44692 q^{4} + 52235 q^{5} - 269570 q^{6} - 403306 q^{7} - 835572 q^{8} + 6590309 q^{9} + 6293062 q^{10} + 3543122 q^{11} - 13901968 q^{12} - 13144282 q^{13} + 59047964 q^{14} - 28781201 q^{15} + 274632904 q^{16} - 158890108 q^{17} + 375018626 q^{18} + 353514772 q^{19} + 604346584 q^{20} - 1280768798 q^{21} + 113379904 q^{22} - 676650377 q^{23} - 2493943332 q^{24} + 4619418649 q^{25} + 1389669452 q^{26} - 1719388235 q^{27} - 4243148928 q^{28} - 446342478 q^{29} - 24300594650 q^{30} - 162880201 q^{31} - 3008635448 q^{32} - 178927661 q^{33} + 40316779096 q^{34} + 13811937902 q^{35} + 28441390948 q^{36} + 18264034717 q^{37} - 66314509704 q^{38} - 62188399676 q^{39} + 128349151956 q^{40} - 83573760394 q^{41} - 687321308 q^{42} - 19058961674 q^{43} + 87678097012 q^{44} + 236060977880 q^{45} - 94682454202 q^{46} + 157105159216 q^{47} - 40045442296 q^{48} - 46501105488 q^{49} - 594826071014 q^{50} + 40699426186 q^{51} + 120848324664 q^{52} - 59030672436 q^{53} - 817100661806 q^{54} + 94146066223 q^{55} + 700443150648 q^{56} + 431483544960 q^{57} - 874554716316 q^{58} + 354857382073 q^{59} + 53910744704 q^{60} - 5964287666 q^{61} + 333569395238 q^{62} - 665848968196 q^{63} - 780082199040 q^{64} + 1819898663264 q^{65} - 759407967626 q^{66} - 635316623835 q^{67} - 134839699256 q^{68} + 843867810617 q^{69} + 1020072749548 q^{70} + 2763810645477 q^{71} + 6706669536384 q^{72} - 3640475737870 q^{73} + 171873845226 q^{74} + 2359433819264 q^{75} - 74679559952 q^{76} + 397775677574 q^{77} - 9685255992536 q^{78} - 7317369377706 q^{79} - 11022394883816 q^{80} + 4175549841428 q^{81} + 8437649428060 q^{82} + 691132076718 q^{83} - 7771401982816 q^{84} + 7466247356866 q^{85} + 1496269999020 q^{86} + 5203404158712 q^{87} - 576175413396 q^{88} + 1451795845365 q^{89} - 17681647010464 q^{90} + 11809188017736 q^{91} + 7358683459328 q^{92} - 15520091057567 q^{93} + 16951236706160 q^{94} - 25364746760184 q^{95} + 2789509579928 q^{96} - 13551704819481 q^{97} - 10415583773112 q^{98} + 6992016441971 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11
11.14.a.a 11.a 1.a $5$ $11.795$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-64\) \(480\) \(-454\) \(-313920\) $+$ $\mathrm{SU}(2)$ \(q+(-13-\beta _{1})q^{2}+(96-2\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
11.14.a.b 11.a 1.a $7$ $11.795$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(379\) \(52689\) \(-89386\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(54+3\beta _{1}-\beta _{2})q^{3}+(6727+\cdots)q^{4}+\cdots\)