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Properties

Label 950.4.a
Level $950$
Weight $4$
Character orbit 950.a
Rep. character $\chi_{950}(1,\cdot)$
Character field $\Q$
Dimension $85$
Newform subspaces $24$
Sturm bound $600$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(600\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(950))\).

Total New Old
Modular forms 462 85 377
Cusp forms 438 85 353
Eisenstein series 24 0 24

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
\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(-\)$-$\(8\)
\(+\)\(-\)\(+\)$-$\(10\)
\(+\)\(-\)\(-\)$+$\(12\)
\(-\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(-\)$+$\(13\)
\(-\)\(-\)\(+\)$+$\(13\)
\(-\)\(-\)\(-\)$-$\(9\)
Plus space\(+\)\(50\)
Minus space\(-\)\(35\)

Trace form

\( 85 q + 2 q^{2} - 8 q^{3} + 340 q^{4} - 20 q^{6} - 8 q^{7} + 8 q^{8} + 775 q^{9} + O(q^{10}) \) \( 85 q + 2 q^{2} - 8 q^{3} + 340 q^{4} - 20 q^{6} - 8 q^{7} + 8 q^{8} + 775 q^{9} + 30 q^{11} - 32 q^{12} + 54 q^{13} + 88 q^{14} + 1360 q^{16} + 134 q^{17} + 202 q^{18} - 19 q^{19} + 608 q^{21} + 168 q^{22} + 282 q^{23} - 80 q^{24} + 168 q^{26} - 320 q^{27} - 32 q^{28} + 486 q^{29} - 148 q^{31} + 32 q^{32} - 524 q^{33} + 156 q^{34} + 3100 q^{36} - 154 q^{37} + 114 q^{38} + 378 q^{39} - 642 q^{41} + 532 q^{42} + 66 q^{43} + 120 q^{44} - 120 q^{46} + 1302 q^{47} - 128 q^{48} + 3345 q^{49} + 4 q^{51} + 216 q^{52} - 650 q^{53} - 140 q^{54} + 352 q^{56} + 114 q^{57} + 104 q^{58} + 976 q^{59} - 2040 q^{61} + 968 q^{62} - 1378 q^{63} + 5440 q^{64} - 24 q^{66} - 140 q^{67} + 536 q^{68} + 5420 q^{69} + 6112 q^{71} + 808 q^{72} + 1410 q^{73} - 2156 q^{74} - 76 q^{76} + 1154 q^{77} - 360 q^{78} - 796 q^{79} + 10549 q^{81} - 748 q^{82} + 244 q^{83} + 2432 q^{84} + 1824 q^{86} + 226 q^{87} + 672 q^{88} + 1326 q^{89} + 128 q^{91} + 1128 q^{92} + 2012 q^{93} + 2576 q^{94} - 320 q^{96} + 2874 q^{97} - 1406 q^{98} + 5506 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(950))\) 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
950.4.a.a 950.a 1.a $1$ $56.052$ \(\Q\) None \(-2\) \(4\) \(0\) \(20\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}-8q^{6}+20q^{7}+\cdots\)
950.4.a.b 950.a 1.a $1$ $56.052$ \(\Q\) None \(2\) \(-2\) \(0\) \(12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+4q^{4}-4q^{6}+12q^{7}+\cdots\)
950.4.a.c 950.a 1.a $1$ $56.052$ \(\Q\) None \(2\) \(2\) \(0\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}-8q^{7}+\cdots\)
950.4.a.d 950.a 1.a $1$ $56.052$ \(\Q\) None \(2\) \(2\) \(0\) \(31\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+31q^{7}+\cdots\)
950.4.a.e 950.a 1.a $2$ $56.052$ \(\Q(\sqrt{73}) \) None \(-4\) \(-9\) \(0\) \(18\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-4-\beta )q^{3}+4q^{4}+(8+2\beta )q^{6}+\cdots\)
950.4.a.f 950.a 1.a $2$ $56.052$ \(\Q(\sqrt{34}) \) None \(-4\) \(0\) \(0\) \(-24\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}+(-12+\cdots)q^{7}+\cdots\)
950.4.a.g 950.a 1.a $2$ $56.052$ \(\Q(\sqrt{3}) \) None \(4\) \(-2\) \(0\) \(-8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1+3\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
950.4.a.h 950.a 1.a $2$ $56.052$ \(\Q(\sqrt{177}) \) None \(4\) \(-1\) \(0\) \(-57\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-\beta q^{3}+4q^{4}-2\beta q^{6}+(-28+\cdots)q^{7}+\cdots\)
950.4.a.i 950.a 1.a $2$ $56.052$ \(\Q(\sqrt{313}) \) None \(4\) \(-1\) \(0\) \(27\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-\beta q^{3}+4q^{4}-2\beta q^{6}+(14+\cdots)q^{7}+\cdots\)
950.4.a.j 950.a 1.a $3$ $56.052$ 3.3.15357.1 None \(-6\) \(-11\) \(0\) \(-29\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-4+\beta _{1})q^{3}+4q^{4}+(8-2\beta _{1}+\cdots)q^{6}+\cdots\)
950.4.a.k 950.a 1.a $3$ $56.052$ 3.3.1257.1 None \(-6\) \(4\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(2-\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-4+\cdots)q^{6}+\cdots\)
950.4.a.l 950.a 1.a $3$ $56.052$ 3.3.16737.1 None \(-6\) \(4\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(-2-2\beta _{1}+\cdots)q^{6}+\cdots\)
950.4.a.m 950.a 1.a $3$ $56.052$ 3.3.5468.1 None \(-6\) \(9\) \(0\) \(11\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(3+\beta _{1})q^{3}+4q^{4}+(-6-2\beta _{1}+\cdots)q^{6}+\cdots\)
950.4.a.n 950.a 1.a $3$ $56.052$ 3.3.1257.1 None \(6\) \(-4\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
950.4.a.o 950.a 1.a $3$ $56.052$ 3.3.16737.1 None \(6\) \(-4\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
950.4.a.p 950.a 1.a $3$ $56.052$ 3.3.126168.1 None \(6\) \(1\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
950.4.a.q 950.a 1.a $6$ $56.052$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(-2\) \(0\) \(-18\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-3+\cdots)q^{7}+\cdots\)
950.4.a.r 950.a 1.a $6$ $56.052$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(-2\) \(0\) \(-18\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2+\cdots)q^{7}+\cdots\)
950.4.a.s 950.a 1.a $6$ $56.052$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(8\) \(0\) \(46\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1+\beta _{2})q^{3}+4q^{4}+(-2-2\beta _{2}+\cdots)q^{6}+\cdots\)
950.4.a.t 950.a 1.a $6$ $56.052$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(-8\) \(0\) \(-46\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1-\beta _{2})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
950.4.a.u 950.a 1.a $6$ $56.052$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(2\) \(0\) \(18\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(3+\cdots)q^{7}+\cdots\)
950.4.a.v 950.a 1.a $6$ $56.052$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(2\) \(0\) \(18\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(2+\cdots)q^{7}+\cdots\)
950.4.a.w 950.a 1.a $7$ $56.052$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-14\) \(-4\) \(0\) \(-24\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
950.4.a.x 950.a 1.a $7$ $56.052$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(4\) \(0\) \(24\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(950))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(950)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)