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Properties

Label 223.2.a
Level $223$
Weight $2$
Character orbit 223.a
Rep. character $\chi_{223}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $3$
Sturm bound $37$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 223.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(37\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(223))\).

Total New Old
Modular forms 19 19 0
Cusp forms 18 18 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.

\(223\)Dim
\(+\)\(6\)
\(-\)\(12\)

Trace form

\( 18 q + q^{2} - 2 q^{3} + 19 q^{4} - 6 q^{6} - 4 q^{7} + 3 q^{8} + 14 q^{9} + O(q^{10}) \) \( 18 q + q^{2} - 2 q^{3} + 19 q^{4} - 6 q^{6} - 4 q^{7} + 3 q^{8} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 4 q^{12} - 4 q^{13} + 6 q^{14} - 12 q^{15} + 33 q^{16} + 4 q^{17} + 7 q^{18} - 2 q^{19} - 10 q^{20} - 18 q^{21} - 10 q^{22} + 4 q^{23} - 32 q^{24} + 4 q^{25} - 20 q^{26} - 26 q^{27} - 28 q^{28} - 4 q^{29} - 20 q^{30} - 4 q^{31} + 17 q^{32} + 12 q^{33} + 20 q^{34} + 2 q^{35} + 15 q^{36} + 2 q^{37} + 8 q^{38} - 10 q^{39} - 12 q^{40} + 14 q^{41} - 2 q^{42} + 4 q^{43} - 20 q^{44} + 12 q^{47} - 38 q^{48} - 12 q^{49} + 19 q^{50} - 4 q^{51} - 16 q^{52} + 10 q^{53} - 38 q^{54} - 10 q^{55} + 11 q^{56} + 20 q^{57} - 7 q^{58} + 10 q^{59} - 58 q^{60} - 24 q^{61} - 3 q^{62} + 20 q^{63} + 67 q^{64} + 36 q^{65} + 42 q^{66} - 49 q^{68} + 12 q^{69} - 10 q^{71} + 41 q^{72} + 18 q^{73} + 20 q^{74} + 17 q^{76} + 34 q^{77} - 8 q^{78} - 20 q^{79} - 46 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{83} - 78 q^{84} + 30 q^{85} + 21 q^{86} + 26 q^{87} - 14 q^{88} - 4 q^{89} + 66 q^{90} - 40 q^{91} + 56 q^{92} + 2 q^{93} + 18 q^{94} - 2 q^{95} - 96 q^{96} - 20 q^{97} - 18 q^{98} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(223))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 223
223.2.a.a 223.a 1.a $2$ $1.781$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
223.2.a.b 223.a 1.a $4$ $1.781$ 4.4.1957.1 None \(-4\) \(0\) \(-3\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
223.2.a.c 223.a 1.a $12$ $1.781$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(7\) \(0\) \(7\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)