Properties

Label 211.2.a
Level 211
Weight 2
Character orbit a
Rep. character \(\chi_{211}(1,\cdot)\)
Character field \(\Q\)
Dimension 17
Newforms 4
Sturm bound 35
Trace bound 2

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Defining parameters

Level: \( N \) = \( 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 211.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(35\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(211))\).

Total New Old
Modular forms 18 18 0
Cusp forms 17 17 0
Eisenstein series 1 1 0

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

\(211\)Dim.
\(+\)\(6\)
\(-\)\(11\)

Trace form

\(17q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(17q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 22q^{20} \) \(\mathstrut +\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 33q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 6q^{32} \) \(\mathstrut -\mathstrut 14q^{33} \) \(\mathstrut -\mathstrut 12q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 36q^{40} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 20q^{44} \) \(\mathstrut +\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 34q^{48} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 30q^{54} \) \(\mathstrut +\mathstrut 25q^{55} \) \(\mathstrut +\mathstrut 36q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 7q^{59} \) \(\mathstrut +\mathstrut 22q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 16q^{62} \) \(\mathstrut +\mathstrut 14q^{63} \) \(\mathstrut -\mathstrut 14q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 34q^{66} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 10q^{69} \) \(\mathstrut +\mathstrut 14q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut -\mathstrut 34q^{72} \) \(\mathstrut +\mathstrut 11q^{73} \) \(\mathstrut +\mathstrut 34q^{74} \) \(\mathstrut -\mathstrut 18q^{75} \) \(\mathstrut -\mathstrut 48q^{76} \) \(\mathstrut -\mathstrut 22q^{77} \) \(\mathstrut +\mathstrut 36q^{78} \) \(\mathstrut +\mathstrut 56q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 42q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 38q^{86} \) \(\mathstrut +\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 48q^{88} \) \(\mathstrut +\mathstrut 22q^{89} \) \(\mathstrut -\mathstrut 90q^{90} \) \(\mathstrut -\mathstrut 34q^{91} \) \(\mathstrut +\mathstrut 42q^{92} \) \(\mathstrut -\mathstrut 46q^{93} \) \(\mathstrut -\mathstrut 18q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut +\mathstrut 36q^{96} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 12q^{98} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(211))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 211
211.2.a.a \(2\) \(1.685\) \(\Q(\sqrt{5}) \) None \(1\) \(3\) \(2\) \(1\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(2+\cdots)q^{5}+\cdots\)
211.2.a.b \(3\) \(1.685\) \(\Q(\zeta_{14})^+\) None \(-2\) \(-1\) \(-8\) \(2\) \(+\) \(q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
211.2.a.c \(3\) \(1.685\) 3.3.229.1 None \(0\) \(-3\) \(-5\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
211.2.a.d \(9\) \(1.685\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-1\) \(-1\) \(15\) \(-2\) \(-\) \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(2+\beta _{3}+\cdots)q^{5}+\cdots\)