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Properties

Label 211.2.a
Level $211$
Weight $2$
Character orbit 211.a
Rep. character $\chi_{211}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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 and the Fricke involution.

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(211))\) into newform subspaces

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