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Properties

Label 203.2.a
Level $203$
Weight $2$
Character orbit 203.a
Rep. character $\chi_{203}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $7$
Sturm bound $40$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 203 = 7 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 203.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(40\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(203))\).

Total New Old
Modular forms 22 15 7
Cusp forms 19 15 4
Eisenstein series 3 0 3

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

\(7\)\(29\)FrickeDim
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(4\)
\(-\)\(+\)$-$\(7\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(4\)
Minus space\(-\)\(11\)

Trace form

\( 15 q + q^{2} - 4 q^{3} + 13 q^{4} + 2 q^{5} + q^{7} + 9 q^{8} + 11 q^{9} + O(q^{10}) \) \( 15 q + q^{2} - 4 q^{3} + 13 q^{4} + 2 q^{5} + q^{7} + 9 q^{8} + 11 q^{9} - 6 q^{10} - 4 q^{11} - 16 q^{12} + 10 q^{13} - q^{14} - 12 q^{15} + 5 q^{16} + 2 q^{17} + 21 q^{18} - 8 q^{19} + 6 q^{20} - 20 q^{22} + 8 q^{23} - 8 q^{24} + 25 q^{25} - 10 q^{26} - 4 q^{27} + 7 q^{28} - 5 q^{29} - 24 q^{30} - 11 q^{32} - 8 q^{33} - 18 q^{34} + 6 q^{35} - 23 q^{36} + 14 q^{37} + 16 q^{38} + 16 q^{39} - 26 q^{40} - 18 q^{41} - 8 q^{42} - 12 q^{43} - 16 q^{44} - 6 q^{45} + 8 q^{46} - 4 q^{47} - 28 q^{48} + 15 q^{49} - 37 q^{50} + 4 q^{51} + 46 q^{52} - 18 q^{53} - 48 q^{54} + 3 q^{56} + 4 q^{57} + q^{58} - 28 q^{59} - 8 q^{60} + 18 q^{61} + 4 q^{62} + q^{63} + 5 q^{64} + 20 q^{65} + 12 q^{66} + 28 q^{67} - 46 q^{68} - 12 q^{69} + 6 q^{70} + 4 q^{71} + 41 q^{72} + 18 q^{73} + 30 q^{74} + 24 q^{75} + 12 q^{76} - 4 q^{77} + 12 q^{79} + 54 q^{80} - 21 q^{81} + 38 q^{82} + 4 q^{83} - 12 q^{84} + 16 q^{85} - 36 q^{86} + 4 q^{87} - 36 q^{88} + 22 q^{89} + 10 q^{90} + 14 q^{91} - 56 q^{92} + 28 q^{93} + 4 q^{94} - 44 q^{95} - 96 q^{96} + 14 q^{97} + q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(203))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 29
203.2.a.a 203.a 1.a $1$ $1.621$ \(\Q\) None \(-2\) \(-1\) \(-4\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-4q^{5}+2q^{6}+\cdots\)
203.2.a.b 203.a 1.a $1$ $1.621$ \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
203.2.a.c 203.a 1.a $1$ $1.621$ \(\Q\) None \(1\) \(2\) \(2\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{5}+2q^{6}+q^{7}+\cdots\)
203.2.a.d 203.a 1.a $2$ $1.621$ \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(3\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}-q^{4}+(2-\beta )q^{5}+\beta q^{6}+\cdots\)
203.2.a.e 203.a 1.a $2$ $1.621$ \(\Q(\sqrt{2}) \) None \(4\) \(2\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1+\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots\)
203.2.a.f 203.a 1.a $3$ $1.621$ 3.3.148.1 None \(-1\) \(-3\) \(-5\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
203.2.a.g 203.a 1.a $5$ $1.621$ 5.5.2626356.1 None \(2\) \(-2\) \(5\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(203))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(203)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)