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Properties

Label 950.2.a
Level $950$
Weight $2$
Character orbit 950.a
Rep. character $\chi_{950}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $14$
Sturm bound $300$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(300\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(950))\).

Total New Old
Modular forms 162 29 133
Cusp forms 139 29 110
Eisenstein series 23 0 23

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

\(2\)\(5\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(5\)
\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(7\)
Minus space\(-\)\(22\)

Trace form

\( 29 q + q^{2} + 4 q^{3} + 29 q^{4} + 6 q^{6} + 6 q^{7} + q^{8} + 47 q^{9} + O(q^{10}) \) \( 29 q + q^{2} + 4 q^{3} + 29 q^{4} + 6 q^{6} + 6 q^{7} + q^{8} + 47 q^{9} + 8 q^{11} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 29 q^{16} - 4 q^{17} - 3 q^{18} + q^{19} - 4 q^{21} + 4 q^{22} - 10 q^{23} + 6 q^{24} - 16 q^{26} + 16 q^{27} + 6 q^{28} + 6 q^{29} + 20 q^{31} + q^{32} - 2 q^{34} + 47 q^{36} + 22 q^{37} - 3 q^{38} + 38 q^{39} - 10 q^{41} - 2 q^{42} - 12 q^{43} + 8 q^{44} + 12 q^{46} - 4 q^{47} + 4 q^{48} + 75 q^{49} + 16 q^{51} + 2 q^{52} + 10 q^{53} + 18 q^{54} + 4 q^{56} - 2 q^{57} + 16 q^{58} + 4 q^{59} + 18 q^{61} + 12 q^{62} + 40 q^{63} + 29 q^{64} - 12 q^{66} - 4 q^{67} - 4 q^{68} - 20 q^{69} - 68 q^{71} - 3 q^{72} - 14 q^{74} + q^{76} - 28 q^{77} - 20 q^{78} + 76 q^{79} + 5 q^{81} + 18 q^{82} + 4 q^{83} - 4 q^{84} - 50 q^{87} + 4 q^{88} - 70 q^{89} + 64 q^{91} - 10 q^{92} - 20 q^{93} + 16 q^{94} + 6 q^{96} + 30 q^{97} - 31 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(950))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 19
950.2.a.a 950.a 1.a $1$ $7.586$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
950.2.a.b 950.a 1.a $1$ $7.586$ \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
950.2.a.c 950.a 1.a $1$ $7.586$ \(\Q\) None \(-1\) \(3\) \(0\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+5q^{7}-q^{8}+\cdots\)
950.2.a.d 950.a 1.a $1$ $7.586$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
950.2.a.e 950.a 1.a $1$ $7.586$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
950.2.a.f 950.a 1.a $2$ $7.586$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
950.2.a.g 950.a 1.a $2$ $7.586$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
950.2.a.h 950.a 1.a $2$ $7.586$ \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}+q^{8}+\cdots\)
950.2.a.i 950.a 1.a $3$ $7.586$ 3.3.568.1 None \(-3\) \(-2\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.j 950.a 1.a $3$ $7.586$ 3.3.993.1 None \(-3\) \(-2\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.k 950.a 1.a $3$ $7.586$ 3.3.257.1 None \(-3\) \(-2\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots\)
950.2.a.l 950.a 1.a $3$ $7.586$ 3.3.993.1 None \(3\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
950.2.a.m 950.a 1.a $3$ $7.586$ 3.3.257.1 None \(3\) \(2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.n 950.a 1.a $3$ $7.586$ 3.3.568.1 None \(3\) \(2\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(950))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(950)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)