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Properties

Label 950.6.a
Level $950$
Weight $6$
Character orbit 950.a
Rep. character $\chi_{950}(1,\cdot)$
Character field $\Q$
Dimension $143$
Newform subspaces $25$
Sturm bound $900$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(900\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(950))\).

Total New Old
Modular forms 762 143 619
Cusp forms 738 143 595
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
\(+\)\(+\)\(+\)$+$\(15\)
\(+\)\(+\)\(-\)$-$\(19\)
\(+\)\(-\)\(+\)$-$\(20\)
\(+\)\(-\)\(-\)$+$\(18\)
\(-\)\(+\)\(+\)$-$\(19\)
\(-\)\(+\)\(-\)$+$\(14\)
\(-\)\(-\)\(+\)$+$\(17\)
\(-\)\(-\)\(-\)$-$\(21\)
Plus space\(+\)\(64\)
Minus space\(-\)\(79\)

Trace form

\( 143 q - 4 q^{2} + 4 q^{3} + 2288 q^{4} - 8 q^{6} - 194 q^{7} - 64 q^{8} + 11929 q^{9} + O(q^{10}) \) \( 143 q - 4 q^{2} + 4 q^{3} + 2288 q^{4} - 8 q^{6} - 194 q^{7} - 64 q^{8} + 11929 q^{9} - 1032 q^{11} + 64 q^{12} - 530 q^{13} - 80 q^{14} + 36608 q^{16} + 1892 q^{17} - 2612 q^{18} + 361 q^{19} - 1180 q^{21} + 1424 q^{22} + 7302 q^{23} - 128 q^{24} + 7920 q^{26} + 12640 q^{27} - 3104 q^{28} + 11466 q^{29} - 2652 q^{31} - 1024 q^{32} + 53416 q^{33} + 21320 q^{34} + 190864 q^{36} + 2458 q^{37} - 4332 q^{38} - 17874 q^{39} + 33498 q^{41} - 9416 q^{42} + 16212 q^{43} - 16512 q^{44} - 3312 q^{46} - 8340 q^{47} + 1024 q^{48} + 344169 q^{49} + 60160 q^{51} - 8480 q^{52} - 70442 q^{53} + 62344 q^{54} - 1280 q^{56} - 6498 q^{57} + 49264 q^{58} + 83380 q^{59} + 23394 q^{61} - 24304 q^{62} - 80872 q^{63} + 585728 q^{64} - 41424 q^{66} + 66860 q^{67} + 30272 q^{68} - 354052 q^{69} - 286868 q^{71} - 41792 q^{72} + 69432 q^{73} + 4792 q^{74} + 5776 q^{76} - 120136 q^{77} + 101040 q^{78} - 98036 q^{79} + 1216855 q^{81} + 62360 q^{82} - 293084 q^{83} - 18880 q^{84} + 46656 q^{86} + 263686 q^{87} + 22784 q^{88} + 262182 q^{89} - 194240 q^{91} + 116832 q^{92} - 287956 q^{93} - 96608 q^{94} - 2048 q^{96} - 239190 q^{97} + 70204 q^{98} + 523708 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(950))\) 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
950.6.a.a 950.a 1.a $1$ $152.365$ \(\Q\) None \(-4\) \(14\) \(0\) \(121\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+14q^{3}+2^{4}q^{4}-56q^{6}+11^{2}q^{7}+\cdots\)
950.6.a.b 950.a 1.a $1$ $152.365$ \(\Q\) None \(4\) \(6\) \(0\) \(27\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+6q^{3}+2^{4}q^{4}+24q^{6}+3^{3}q^{7}+\cdots\)
950.6.a.c 950.a 1.a $1$ $152.365$ \(\Q\) None \(4\) \(16\) \(0\) \(44\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+2^{4}q^{3}+2^{4}q^{4}+2^{6}q^{6}+44q^{7}+\cdots\)
950.6.a.d 950.a 1.a $2$ $152.365$ \(\Q(\sqrt{1441}) \) None \(8\) \(-3\) \(0\) \(-114\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-1-\beta )q^{3}+2^{4}q^{4}+(-4+\cdots)q^{6}+\cdots\)
950.6.a.e 950.a 1.a $2$ $152.365$ \(\Q(\sqrt{163}) \) None \(8\) \(2\) \(0\) \(-156\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(1+\beta )q^{3}+2^{4}q^{4}+(4+4\beta )q^{6}+\cdots\)
950.6.a.f 950.a 1.a $3$ $152.365$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(-13\) \(0\) \(-228\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-4-\beta _{1})q^{3}+2^{4}q^{4}+(2^{4}+\cdots)q^{6}+\cdots\)
950.6.a.g 950.a 1.a $3$ $152.365$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(-8\) \(0\) \(-218\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-3+\beta _{1})q^{3}+2^{4}q^{4}+(12+\cdots)q^{6}+\cdots\)
950.6.a.h 950.a 1.a $3$ $152.365$ 3.3.57912.1 None \(-12\) \(22\) \(0\) \(272\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(8+\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
950.6.a.i 950.a 1.a $3$ $152.365$ 3.3.171768.1 None \(12\) \(-32\) \(0\) \(58\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-11-\beta _{2})q^{3}+2^{4}q^{4}+(-44+\cdots)q^{6}+\cdots\)
950.6.a.j 950.a 1.a $4$ $152.365$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(19\) \(0\) \(27\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
950.6.a.k 950.a 1.a $4$ $152.365$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(-23\) \(0\) \(107\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-6+\beta _{1})q^{3}+2^{4}q^{4}+(-24+\cdots)q^{6}+\cdots\)
950.6.a.l 950.a 1.a $5$ $152.365$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(-23\) \(0\) \(-71\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-5+\beta _{1})q^{3}+2^{4}q^{4}+(20+\cdots)q^{6}+\cdots\)
950.6.a.m 950.a 1.a $5$ $152.365$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(27\) \(0\) \(-63\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(5+\beta _{1})q^{3}+2^{4}q^{4}+(20+4\beta _{1}+\cdots)q^{6}+\cdots\)
950.6.a.n 950.a 1.a $6$ $152.365$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(14\) \(0\) \(54\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(2+\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.o 950.a 1.a $6$ $152.365$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(14\) \(0\) \(54\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(2+\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.p 950.a 1.a $6$ $152.365$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(24\) \(-14\) \(0\) \(-54\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-2-\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.q 950.a 1.a $6$ $152.365$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(24\) \(-14\) \(0\) \(-54\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-2-\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.r 950.a 1.a $9$ $152.365$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-36\) \(-4\) \(0\) \(-44\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.s 950.a 1.a $9$ $152.365$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-36\) \(-4\) \(0\) \(-44\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.t 950.a 1.a $9$ $152.365$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(36\) \(4\) \(0\) \(44\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.u 950.a 1.a $9$ $152.365$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(36\) \(4\) \(0\) \(44\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.v 950.a 1.a $11$ $152.365$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-44\) \(4\) \(0\) \(240\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}-4\beta _{1}q^{6}+\cdots\)
950.6.a.w 950.a 1.a $11$ $152.365$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(44\) \(-4\) \(0\) \(-240\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}-4\beta _{1}q^{6}+\cdots\)
950.6.a.x 950.a 1.a $12$ $152.365$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-48\) \(-32\) \(0\) \(-250\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-3+\beta _{1})q^{3}+2^{4}q^{4}+(12+\cdots)q^{6}+\cdots\)
950.6.a.y 950.a 1.a $12$ $152.365$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(48\) \(32\) \(0\) \(250\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(3-\beta _{1})q^{3}+2^{4}q^{4}+(12-4\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(950))\) into lower level spaces

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