Properties

Label 11.10.a
Level 11
Weight 10
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 2
Sturm bound 10
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 11.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(11))\).

Total New Old
Modular forms 10 8 2
Cusp forms 8 8 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.

\(11\)Dim.
\(+\)\(3\)
\(-\)\(5\)

Trace form

\(8q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 74q^{3} \) \(\mathstrut +\mathstrut 1620q^{4} \) \(\mathstrut -\mathstrut 230q^{5} \) \(\mathstrut -\mathstrut 578q^{6} \) \(\mathstrut +\mathstrut 1140q^{7} \) \(\mathstrut +\mathstrut 20652q^{8} \) \(\mathstrut +\mathstrut 89342q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 74q^{3} \) \(\mathstrut +\mathstrut 1620q^{4} \) \(\mathstrut -\mathstrut 230q^{5} \) \(\mathstrut -\mathstrut 578q^{6} \) \(\mathstrut +\mathstrut 1140q^{7} \) \(\mathstrut +\mathstrut 20652q^{8} \) \(\mathstrut +\mathstrut 89342q^{9} \) \(\mathstrut -\mathstrut 83738q^{10} \) \(\mathstrut +\mathstrut 29282q^{11} \) \(\mathstrut +\mathstrut 39248q^{12} \) \(\mathstrut -\mathstrut 46044q^{13} \) \(\mathstrut +\mathstrut 24412q^{14} \) \(\mathstrut -\mathstrut 19106q^{15} \) \(\mathstrut -\mathstrut 432120q^{16} \) \(\mathstrut -\mathstrut 528560q^{17} \) \(\mathstrut +\mathstrut 1174610q^{18} \) \(\mathstrut -\mathstrut 1190296q^{19} \) \(\mathstrut -\mathstrut 2069896q^{20} \) \(\mathstrut -\mathstrut 462428q^{21} \) \(\mathstrut +\mathstrut 234256q^{22} \) \(\mathstrut +\mathstrut 5090582q^{23} \) \(\mathstrut +\mathstrut 488700q^{24} \) \(\mathstrut +\mathstrut 4604214q^{25} \) \(\mathstrut +\mathstrut 3194668q^{26} \) \(\mathstrut -\mathstrut 5045294q^{27} \) \(\mathstrut -\mathstrut 5047520q^{28} \) \(\mathstrut +\mathstrut 3174756q^{29} \) \(\mathstrut +\mathstrut 4505830q^{30} \) \(\mathstrut +\mathstrut 7205094q^{31} \) \(\mathstrut -\mathstrut 18294040q^{32} \) \(\mathstrut +\mathstrut 4363018q^{33} \) \(\mathstrut -\mathstrut 5679944q^{34} \) \(\mathstrut -\mathstrut 14501708q^{35} \) \(\mathstrut -\mathstrut 5775164q^{36} \) \(\mathstrut -\mathstrut 1798954q^{37} \) \(\mathstrut +\mathstrut 1039992q^{38} \) \(\mathstrut +\mathstrut 54037792q^{39} \) \(\mathstrut -\mathstrut 27552684q^{40} \) \(\mathstrut -\mathstrut 4175684q^{41} \) \(\mathstrut -\mathstrut 73685276q^{42} \) \(\mathstrut +\mathstrut 47957684q^{43} \) \(\mathstrut -\mathstrut 2986764q^{44} \) \(\mathstrut -\mathstrut 23906560q^{45} \) \(\mathstrut -\mathstrut 21202042q^{46} \) \(\mathstrut +\mathstrut 2547848q^{47} \) \(\mathstrut +\mathstrut 173389640q^{48} \) \(\mathstrut +\mathstrut 52376928q^{49} \) \(\mathstrut +\mathstrut 188003306q^{50} \) \(\mathstrut -\mathstrut 197964644q^{51} \) \(\mathstrut +\mathstrut 98761240q^{52} \) \(\mathstrut -\mathstrut 41405544q^{53} \) \(\mathstrut -\mathstrut 248932046q^{54} \) \(\mathstrut +\mathstrut 50042938q^{55} \) \(\mathstrut +\mathstrut 35350008q^{56} \) \(\mathstrut -\mathstrut 300438024q^{57} \) \(\mathstrut -\mathstrut 57004092q^{58} \) \(\mathstrut +\mathstrut 345886082q^{59} \) \(\mathstrut +\mathstrut 81928544q^{60} \) \(\mathstrut +\mathstrut 225292700q^{61} \) \(\mathstrut -\mathstrut 248605562q^{62} \) \(\mathstrut -\mathstrut 117057784q^{63} \) \(\mathstrut -\mathstrut 467302720q^{64} \) \(\mathstrut -\mathstrut 496809896q^{65} \) \(\mathstrut +\mathstrut 312351094q^{66} \) \(\mathstrut +\mathstrut 653677834q^{67} \) \(\mathstrut -\mathstrut 1061562904q^{68} \) \(\mathstrut -\mathstrut 165010498q^{69} \) \(\mathstrut +\mathstrut 1585529068q^{70} \) \(\mathstrut -\mathstrut 48179694q^{71} \) \(\mathstrut +\mathstrut 1470546336q^{72} \) \(\mathstrut -\mathstrut 299529612q^{73} \) \(\mathstrut -\mathstrut 452221206q^{74} \) \(\mathstrut -\mathstrut 1525780696q^{75} \) \(\mathstrut -\mathstrut 841669744q^{76} \) \(\mathstrut +\mathstrut 229278060q^{77} \) \(\mathstrut +\mathstrut 2174191720q^{78} \) \(\mathstrut -\mathstrut 1467250820q^{79} \) \(\mathstrut +\mathstrut 17771864q^{80} \) \(\mathstrut +\mathstrut 3123036200q^{81} \) \(\mathstrut +\mathstrut 289855036q^{82} \) \(\mathstrut +\mathstrut 1618138740q^{83} \) \(\mathstrut -\mathstrut 3190963840q^{84} \) \(\mathstrut +\mathstrut 827755396q^{85} \) \(\mathstrut -\mathstrut 1505983188q^{86} \) \(\mathstrut -\mathstrut 2316789168q^{87} \) \(\mathstrut +\mathstrut 889879980q^{88} \) \(\mathstrut +\mathstrut 152250798q^{89} \) \(\mathstrut -\mathstrut 7038414304q^{90} \) \(\mathstrut -\mathstrut 1260663328q^{91} \) \(\mathstrut +\mathstrut 5457058144q^{92} \) \(\mathstrut +\mathstrut 1764718990q^{93} \) \(\mathstrut +\mathstrut 5948451440q^{94} \) \(\mathstrut -\mathstrut 2704939944q^{95} \) \(\mathstrut +\mathstrut 1363238456q^{96} \) \(\mathstrut -\mathstrut 2447938502q^{97} \) \(\mathstrut -\mathstrut 3560544360q^{98} \) \(\mathstrut +\mathstrut 881915276q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(11))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.10.a.a \(3\) \(5.665\) 3.3.2659452.1 None \(0\) \(-186\) \(-1824\) \(-7260\) \(+\) \(q-\beta _{1}q^{2}+(-62+4\beta _{1}-\beta _{2})q^{3}+(304+\cdots)q^{4}+\cdots\)
11.10.a.b \(5\) \(5.665\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(16\) \(112\) \(1594\) \(8400\) \(-\) \(q+(3+\beta _{1})q^{2}+(22+3\beta _{1}+\beta _{4})q^{3}+\cdots\)