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

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

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(950))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 19
950.6.a.a \(1\) \(152.365\) \(\Q\) None \(-4\) \(14\) \(0\) \(121\) \(+\) \(+\) \(-\) \(q-4q^{2}+14q^{3}+2^{4}q^{4}-56q^{6}+11^{2}q^{7}+\cdots\)
950.6.a.b \(1\) \(152.365\) \(\Q\) None \(4\) \(6\) \(0\) \(27\) \(-\) \(+\) \(+\) \(q+4q^{2}+6q^{3}+2^{4}q^{4}+24q^{6}+3^{3}q^{7}+\cdots\)
950.6.a.c \(1\) \(152.365\) \(\Q\) None \(4\) \(16\) \(0\) \(44\) \(-\) \(+\) \(-\) \(q+4q^{2}+2^{4}q^{3}+2^{4}q^{4}+2^{6}q^{6}+44q^{7}+\cdots\)
950.6.a.d \(2\) \(152.365\) \(\Q(\sqrt{1441}) \) None \(8\) \(-3\) \(0\) \(-114\) \(-\) \(+\) \(-\) \(q+4q^{2}+(-1-\beta )q^{3}+2^{4}q^{4}+(-4+\cdots)q^{6}+\cdots\)
950.6.a.e \(2\) \(152.365\) \(\Q(\sqrt{163}) \) None \(8\) \(2\) \(0\) \(-156\) \(-\) \(+\) \(-\) \(q+4q^{2}+(1+\beta )q^{3}+2^{4}q^{4}+(4+4\beta )q^{6}+\cdots\)
950.6.a.f \(3\) \(152.365\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(-13\) \(0\) \(-228\) \(+\) \(+\) \(+\) \(q-4q^{2}+(-4-\beta _{1})q^{3}+2^{4}q^{4}+(2^{4}+\cdots)q^{6}+\cdots\)
950.6.a.g \(3\) \(152.365\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(-8\) \(0\) \(-218\) \(+\) \(+\) \(+\) \(q-4q^{2}+(-3+\beta _{1})q^{3}+2^{4}q^{4}+(12+\cdots)q^{6}+\cdots\)
950.6.a.h \(3\) \(152.365\) 3.3.57912.1 None \(-12\) \(22\) \(0\) \(272\) \(+\) \(+\) \(+\) \(q-4q^{2}+(8+\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
950.6.a.i \(3\) \(152.365\) 3.3.171768.1 None \(12\) \(-32\) \(0\) \(58\) \(-\) \(+\) \(-\) \(q+4q^{2}+(-11-\beta _{2})q^{3}+2^{4}q^{4}+(-44+\cdots)q^{6}+\cdots\)
950.6.a.j \(4\) \(152.365\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(19\) \(0\) \(27\) \(+\) \(+\) \(-\) \(q-4q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
950.6.a.k \(4\) \(152.365\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(-23\) \(0\) \(107\) \(-\) \(+\) \(+\) \(q+4q^{2}+(-6+\beta _{1})q^{3}+2^{4}q^{4}+(-24+\cdots)q^{6}+\cdots\)
950.6.a.l \(5\) \(152.365\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(-23\) \(0\) \(-71\) \(+\) \(+\) \(-\) \(q-4q^{2}+(-5+\beta _{1})q^{3}+2^{4}q^{4}+(20+\cdots)q^{6}+\cdots\)
950.6.a.m \(5\) \(152.365\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(27\) \(0\) \(-63\) \(-\) \(+\) \(+\) \(q+4q^{2}+(5+\beta _{1})q^{3}+2^{4}q^{4}+(20+4\beta _{1}+\cdots)q^{6}+\cdots\)
950.6.a.n \(6\) \(152.365\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(14\) \(0\) \(54\) \(+\) \(+\) \(+\) \(q-4q^{2}+(2+\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.o \(6\) \(152.365\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(14\) \(0\) \(54\) \(+\) \(-\) \(-\) \(q-4q^{2}+(2+\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.p \(6\) \(152.365\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(24\) \(-14\) \(0\) \(-54\) \(-\) \(-\) \(+\) \(q+4q^{2}+(-2-\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.q \(6\) \(152.365\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(24\) \(-14\) \(0\) \(-54\) \(-\) \(+\) \(-\) \(q+4q^{2}+(-2-\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{6}+\cdots\)
950.6.a.r \(9\) \(152.365\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-36\) \(-4\) \(0\) \(-44\) \(+\) \(-\) \(+\) \(q-4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.s \(9\) \(152.365\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-36\) \(-4\) \(0\) \(-44\) \(+\) \(+\) \(-\) \(q-4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.t \(9\) \(152.365\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(36\) \(4\) \(0\) \(44\) \(-\) \(+\) \(+\) \(q+4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.u \(9\) \(152.365\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(36\) \(4\) \(0\) \(44\) \(-\) \(-\) \(-\) \(q+4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+4\beta _{1}q^{6}+\cdots\)
950.6.a.v \(11\) \(152.365\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-44\) \(4\) \(0\) \(240\) \(+\) \(-\) \(+\) \(q-4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}-4\beta _{1}q^{6}+\cdots\)
950.6.a.w \(11\) \(152.365\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(44\) \(-4\) \(0\) \(-240\) \(-\) \(-\) \(+\) \(q+4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}-4\beta _{1}q^{6}+\cdots\)
950.6.a.x \(12\) \(152.365\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-48\) \(-32\) \(0\) \(-250\) \(+\) \(-\) \(-\) \(q-4q^{2}+(-3+\beta _{1})q^{3}+2^{4}q^{4}+(12+\cdots)q^{6}+\cdots\)
950.6.a.y \(12\) \(152.365\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(48\) \(32\) \(0\) \(250\) \(-\) \(-\) \(-\) \(q+4q^{2}+(3-\beta _{1})q^{3}+2^{4}q^{4}+(12-4\beta _{1}+\cdots)q^{6}+\cdots\)

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

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