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Properties

Label 191.2.a
Level $191$
Weight $2$
Character orbit 191.a
Rep. character $\chi_{191}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 191.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(191))\).

Total New Old
Modular forms 17 17 0
Cusp forms 16 16 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.

\(191\)Dim
\(+\)\(2\)
\(-\)\(14\)

Trace form

\( 16 q - q^{2} + 17 q^{4} + 6 q^{6} + 2 q^{7} - 3 q^{8} + 18 q^{9} + O(q^{10}) \) \( 16 q - q^{2} + 17 q^{4} + 6 q^{6} + 2 q^{7} - 3 q^{8} + 18 q^{9} + 6 q^{10} - 4 q^{11} - 2 q^{12} + 12 q^{13} - 12 q^{14} - 6 q^{15} + 15 q^{16} + 14 q^{17} - 15 q^{18} + 14 q^{19} - 16 q^{20} + 10 q^{21} - 4 q^{22} - 14 q^{23} - 12 q^{24} + 20 q^{25} + 8 q^{26} + 12 q^{27} - 14 q^{28} + 6 q^{29} - 44 q^{30} + 10 q^{31} - 17 q^{32} + 2 q^{33} - 6 q^{34} - 14 q^{35} - 9 q^{36} - 6 q^{37} - 36 q^{38} - 10 q^{39} + 4 q^{40} + 8 q^{41} - 72 q^{42} + 12 q^{43} - 58 q^{44} - 34 q^{45} - 14 q^{46} - 22 q^{47} - 49 q^{48} + 42 q^{49} - 14 q^{50} - 12 q^{51} + 26 q^{52} - 4 q^{53} - q^{54} + 14 q^{55} - 14 q^{56} - 10 q^{57} - 4 q^{58} + 20 q^{59} - 9 q^{60} + 28 q^{61} + 6 q^{62} - 10 q^{63} + 33 q^{64} - 4 q^{65} + 20 q^{66} - 16 q^{67} + 55 q^{68} + 26 q^{69} - 22 q^{71} - 27 q^{72} + 38 q^{73} + 14 q^{74} - 6 q^{75} + 50 q^{76} - 8 q^{77} + 3 q^{78} + 20 q^{79} + 14 q^{80} + 48 q^{81} - 6 q^{82} - 10 q^{83} + 78 q^{84} - 4 q^{85} + 32 q^{86} - 18 q^{87} - 4 q^{89} + 27 q^{90} - 22 q^{91} - 64 q^{92} + 12 q^{93} + 74 q^{94} - 2 q^{95} + 6 q^{96} + 14 q^{97} + 17 q^{98} - 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(191))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 191
191.2.a.a 191.a 1.a $2$ $1.525$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
191.2.a.b 191.a 1.a $14$ $1.525$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(2\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)