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Properties

Label 11.18.a
Level $11$
Weight $18$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(11))\).

Total New Old
Modular forms 18 14 4
Cusp forms 16 14 2
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
\(+\)\(6\)
\(-\)\(8\)

Trace form

\( 14 q + 256 q^{2} + 14923 q^{3} + 742356 q^{4} + 2143225 q^{5} - 3132290 q^{6} - 32210994 q^{7} - 169575060 q^{8} + 791185313 q^{9} + O(q^{10}) \) \( 14 q + 256 q^{2} + 14923 q^{3} + 742356 q^{4} + 2143225 q^{5} - 3132290 q^{6} - 32210994 q^{7} - 169575060 q^{8} + 791185313 q^{9} - 861657338 q^{10} + 428717762 q^{11} + 1228666256 q^{12} - 5315878242 q^{13} + 16027361116 q^{14} - 10675067621 q^{15} + 77100430728 q^{16} - 12568378784 q^{17} - 178774689022 q^{18} - 38212814812 q^{19} + 474700670264 q^{20} + 21505140670 q^{21} + 54875873536 q^{22} + 395228531123 q^{23} - 247749367620 q^{24} + 714382227609 q^{25} + 3637172134732 q^{26} + 3435495020485 q^{27} - 6996666671648 q^{28} - 2161609519518 q^{29} + 23729435978470 q^{30} + 21680999365299 q^{31} - 41752737014104 q^{32} - 1887858664967 q^{33} - 12085365294056 q^{34} - 29911990256738 q^{35} + 110745672051460 q^{36} - 39413281527649 q^{37} + 67522857003960 q^{38} - 110541513463628 q^{39} - 89994337567404 q^{40} - 127836179303162 q^{41} - 129400067620508 q^{42} + 65557181570678 q^{43} + 8640377775348 q^{44} + 148886584348220 q^{45} - 82721154788218 q^{46} + 98786156177576 q^{47} - 88998545904952 q^{48} - 39257177051958 q^{49} + 165614011796666 q^{50} + 1007756004568138 q^{51} - 2280136835154344 q^{52} - 747083391773232 q^{53} + 578326602177778 q^{54} + 310229390015083 q^{55} + 4601666662665336 q^{56} + 828264084781680 q^{57} + 3351054723977700 q^{58} - 330789409332511 q^{59} - 7849085771376736 q^{60} - 885930878698234 q^{61} + 752417982310342 q^{62} - 4809871701885172 q^{63} + 10320980074300736 q^{64} - 1304619050094776 q^{65} + 6317939490421174 q^{66} + 3673252853893261 q^{67} - 3850125064919128 q^{68} + 7294733886432887 q^{69} + 6026856416590828 q^{70} - 1753725410819247 q^{71} - 63583360653509280 q^{72} + 17779735621718058 q^{73} + 2734346351497290 q^{74} - 9256718326117576 q^{75} - 56316214638363568 q^{76} + 6520425461720346 q^{77} + 56567096750634856 q^{78} + 295503325769470 q^{79} + 8811745462873304 q^{80} + 6915984877138118 q^{81} + 20331813702226972 q^{82} - 10007567692170642 q^{83} + 77587544817624512 q^{84} - 92346214829037914 q^{85} - 150491514706228500 q^{86} + 65889305647044840 q^{87} - 7243139430036180 q^{88} + 115884658255441131 q^{89} + 123858103739893376 q^{90} + 78344445359629640 q^{91} + 77157441070657696 q^{92} - 83086322305592849 q^{93} + 37484597900811632 q^{94} - 51142432157773224 q^{95} - 23110304657018632 q^{96} + 205607627319123001 q^{97} - 240721826266328568 q^{98} + 7648241488475291 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(11))\) 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
11.18.a.a 11.a 1.a $6$ $20.154$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(11865\) \(347991\) \(-31314630\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1977+14\beta _{1}-\beta _{2})q^{3}+\cdots\)
11.18.a.b 11.a 1.a $8$ $20.154$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(256\) \(3058\) \(1795234\) \(-896364\) $-$ $\mathrm{SU}(2)$ \(q+(2^{5}-\beta _{1})q^{2}+(382-9\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(11))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(11)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)