Properties

Label 11.12.a
Level 11
Weight 12
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 11.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(11))\).

Total New Old
Modular forms 12 8 4
Cusp forms 10 8 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.

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

Trace form

\(8q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut -\mathstrut 233q^{3} \) \(\mathstrut +\mathstrut 9076q^{4} \) \(\mathstrut -\mathstrut 15703q^{5} \) \(\mathstrut +\mathstrut 10942q^{6} \) \(\mathstrut +\mathstrut 73958q^{7} \) \(\mathstrut -\mathstrut 56676q^{8} \) \(\mathstrut +\mathstrut 307703q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut -\mathstrut 233q^{3} \) \(\mathstrut +\mathstrut 9076q^{4} \) \(\mathstrut -\mathstrut 15703q^{5} \) \(\mathstrut +\mathstrut 10942q^{6} \) \(\mathstrut +\mathstrut 73958q^{7} \) \(\mathstrut -\mathstrut 56676q^{8} \) \(\mathstrut +\mathstrut 307703q^{9} \) \(\mathstrut +\mathstrut 449510q^{10} \) \(\mathstrut -\mathstrut 322102q^{11} \) \(\mathstrut +\mathstrut 1431584q^{12} \) \(\mathstrut +\mathstrut 1964714q^{13} \) \(\mathstrut +\mathstrut 1988732q^{14} \) \(\mathstrut -\mathstrut 2772689q^{15} \) \(\mathstrut +\mathstrut 3418600q^{16} \) \(\mathstrut +\mathstrut 16395044q^{17} \) \(\mathstrut -\mathstrut 20821822q^{18} \) \(\mathstrut -\mathstrut 19590492q^{19} \) \(\mathstrut +\mathstrut 6760168q^{20} \) \(\mathstrut +\mathstrut 17398534q^{21} \) \(\mathstrut -\mathstrut 5153632q^{22} \) \(\mathstrut -\mathstrut 94440641q^{23} \) \(\mathstrut -\mathstrut 83441748q^{24} \) \(\mathstrut +\mathstrut 44566651q^{25} \) \(\mathstrut -\mathstrut 125238196q^{26} \) \(\mathstrut +\mathstrut 209008465q^{27} \) \(\mathstrut +\mathstrut 200526736q^{28} \) \(\mathstrut -\mathstrut 476100402q^{29} \) \(\mathstrut +\mathstrut 240810694q^{30} \) \(\mathstrut +\mathstrut 371580791q^{31} \) \(\mathstrut +\mathstrut 908210584q^{32} \) \(\mathstrut -\mathstrut 89061203q^{33} \) \(\mathstrut -\mathstrut 1102433800q^{34} \) \(\mathstrut +\mathstrut 254817638q^{35} \) \(\mathstrut -\mathstrut 653073836q^{36} \) \(\mathstrut +\mathstrut 422778399q^{37} \) \(\mathstrut +\mathstrut 534201048q^{38} \) \(\mathstrut +\mathstrut 1255438660q^{39} \) \(\mathstrut -\mathstrut 1542772332q^{40} \) \(\mathstrut +\mathstrut 504799778q^{41} \) \(\mathstrut -\mathstrut 1024191356q^{42} \) \(\mathstrut -\mathstrut 49493922q^{43} \) \(\mathstrut -\mathstrut 541775564q^{44} \) \(\mathstrut -\mathstrut 5756032q^{45} \) \(\mathstrut +\mathstrut 472149670q^{46} \) \(\mathstrut -\mathstrut 4355376128q^{47} \) \(\mathstrut -\mathstrut 3141381208q^{48} \) \(\mathstrut +\mathstrut 2557152516q^{49} \) \(\mathstrut -\mathstrut 4723225718q^{50} \) \(\mathstrut +\mathstrut 8840429458q^{51} \) \(\mathstrut -\mathstrut 1951902872q^{52} \) \(\mathstrut +\mathstrut 4727609532q^{53} \) \(\mathstrut -\mathstrut 5957610494q^{54} \) \(\mathstrut +\mathstrut 176028743q^{55} \) \(\mathstrut +\mathstrut 7812077208q^{56} \) \(\mathstrut +\mathstrut 6252115680q^{57} \) \(\mathstrut +\mathstrut 11275380132q^{58} \) \(\mathstrut +\mathstrut 5320998277q^{59} \) \(\mathstrut -\mathstrut 5610203728q^{60} \) \(\mathstrut -\mathstrut 26469446814q^{61} \) \(\mathstrut +\mathstrut 16803218966q^{62} \) \(\mathstrut -\mathstrut 12584866468q^{63} \) \(\mathstrut +\mathstrut 6698319968q^{64} \) \(\mathstrut +\mathstrut 5207837360q^{65} \) \(\mathstrut +\mathstrut 448688086q^{66} \) \(\mathstrut +\mathstrut 33465935785q^{67} \) \(\mathstrut +\mathstrut 2291826712q^{68} \) \(\mathstrut +\mathstrut 5424714107q^{69} \) \(\mathstrut -\mathstrut 53189453716q^{70} \) \(\mathstrut -\mathstrut 49169436051q^{71} \) \(\mathstrut -\mathstrut 46682928432q^{72} \) \(\mathstrut +\mathstrut 10272916070q^{73} \) \(\mathstrut -\mathstrut 21440089350q^{74} \) \(\mathstrut +\mathstrut 35944240640q^{75} \) \(\mathstrut +\mathstrut 109723150848q^{76} \) \(\mathstrut -\mathstrut 13547932222q^{77} \) \(\mathstrut -\mathstrut 99909542648q^{78} \) \(\mathstrut +\mathstrut 36156478486q^{79} \) \(\mathstrut +\mathstrut 2843409976q^{80} \) \(\mathstrut -\mathstrut 127998534496q^{81} \) \(\mathstrut +\mathstrut 88813826300q^{82} \) \(\mathstrut -\mathstrut 41341594746q^{83} \) \(\mathstrut +\mathstrut 70613000912q^{84} \) \(\mathstrut +\mathstrut 89181763862q^{85} \) \(\mathstrut +\mathstrut 170675303052q^{86} \) \(\mathstrut +\mathstrut 30444967224q^{87} \) \(\mathstrut -\mathstrut 79988878068q^{88} \) \(\mathstrut -\mathstrut 123823053765q^{89} \) \(\mathstrut +\mathstrut 336287620112q^{90} \) \(\mathstrut -\mathstrut 9388521112q^{91} \) \(\mathstrut -\mathstrut 416009937424q^{92} \) \(\mathstrut +\mathstrut 1013667979q^{93} \) \(\mathstrut -\mathstrut 109248658064q^{94} \) \(\mathstrut +\mathstrut 67395785832q^{95} \) \(\mathstrut +\mathstrut 153846148520q^{96} \) \(\mathstrut +\mathstrut 162861068113q^{97} \) \(\mathstrut +\mathstrut 310631219304q^{98} \) \(\mathstrut -\mathstrut 113395848049q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(11))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.12.a.a \(3\) \(8.452\) 3.3.202533.1 None \(0\) \(-393\) \(-7305\) \(-5082\) \(-\) \(q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots\)
11.12.a.b \(5\) \(8.452\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(32\) \(160\) \(-8398\) \(79040\) \(+\) \(q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(11))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(11)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)