Properties

Label 150.6.a
Level $150$
Weight $6$
Character orbit 150.a
Rep. character $\chi_{150}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $15$
Sturm bound $180$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(180\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(150))\).

Total New Old
Modular forms 162 17 145
Cusp forms 138 17 121
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.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(7\)
Minus space\(-\)\(10\)

Trace form

\( 17q - 4q^{2} - 9q^{3} + 272q^{4} + 36q^{6} - 372q^{7} - 64q^{8} + 1377q^{9} + O(q^{10}) \) \( 17q - 4q^{2} - 9q^{3} + 272q^{4} + 36q^{6} - 372q^{7} - 64q^{8} + 1377q^{9} - 652q^{11} - 144q^{12} + 114q^{13} - 1056q^{14} + 4352q^{16} + 3558q^{17} - 324q^{18} - 5492q^{19} + 360q^{21} + 3072q^{22} + 5424q^{23} + 576q^{24} - 2440q^{26} - 729q^{27} - 5952q^{28} + 13542q^{29} + 15952q^{31} - 1024q^{32} - 7128q^{33} + 19944q^{34} + 22032q^{36} + 3378q^{37} + 1840q^{38} + 342q^{39} - 1030q^{41} + 11088q^{42} - 22476q^{43} - 10432q^{44} + 8736q^{46} + 7248q^{47} - 2304q^{48} + 36585q^{49} + 35010q^{51} + 1824q^{52} + 33234q^{53} + 2916q^{54} - 16896q^{56} + 14940q^{57} + 12120q^{58} + 8980q^{59} + 108598q^{61} - 3008q^{62} - 30132q^{63} + 69632q^{64} + 9648q^{66} + 49188q^{67} + 56928q^{68} + 16056q^{69} - 102072q^{71} - 5184q^{72} - 72726q^{73} - 10344q^{74} - 87872q^{76} - 107904q^{77} + 6984q^{78} - 151856q^{79} + 111537q^{81} - 53928q^{82} - 39996q^{83} + 5760q^{84} - 126672q^{86} + 114750q^{87} + 49152q^{88} + 47114q^{89} + 60704q^{91} + 86784q^{92} - 86688q^{93} - 33408q^{94} + 9216q^{96} - 126342q^{97} + 46812q^{98} - 52812q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(150))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
150.6.a.a \(1\) \(24.058\) \(\Q\) None \(-4\) \(-9\) \(0\) \(-47\) \(+\) \(+\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}-47q^{7}+\cdots\)
150.6.a.b \(1\) \(24.058\) \(\Q\) None \(-4\) \(-9\) \(0\) \(-32\) \(+\) \(+\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}-2^{5}q^{7}+\cdots\)
150.6.a.c \(1\) \(24.058\) \(\Q\) None \(-4\) \(-9\) \(0\) \(233\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}+233q^{7}+\cdots\)
150.6.a.d \(1\) \(24.058\) \(\Q\) None \(-4\) \(9\) \(0\) \(-176\) \(+\) \(-\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}-176q^{7}+\cdots\)
150.6.a.e \(1\) \(24.058\) \(\Q\) None \(-4\) \(9\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}-q^{7}+\cdots\)
150.6.a.f \(1\) \(24.058\) \(\Q\) None \(-4\) \(9\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}+4q^{7}+\cdots\)
150.6.a.g \(1\) \(24.058\) \(\Q\) None \(-4\) \(9\) \(0\) \(79\) \(+\) \(-\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}+79q^{7}+\cdots\)
150.6.a.h \(1\) \(24.058\) \(\Q\) None \(4\) \(-9\) \(0\) \(-164\) \(-\) \(+\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}-164q^{7}+\cdots\)
150.6.a.i \(1\) \(24.058\) \(\Q\) None \(4\) \(-9\) \(0\) \(-79\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}-79q^{7}+\cdots\)
150.6.a.j \(1\) \(24.058\) \(\Q\) None \(4\) \(-9\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}-4q^{7}+\cdots\)
150.6.a.k \(1\) \(24.058\) \(\Q\) None \(4\) \(-9\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}+q^{7}+\cdots\)
150.6.a.l \(1\) \(24.058\) \(\Q\) None \(4\) \(9\) \(0\) \(-233\) \(-\) \(-\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+6^{2}q^{6}-233q^{7}+\cdots\)
150.6.a.m \(1\) \(24.058\) \(\Q\) None \(4\) \(9\) \(0\) \(47\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+6^{2}q^{6}+47q^{7}+\cdots\)
150.6.a.n \(2\) \(24.058\) \(\Q(\sqrt{1249}) \) None \(-8\) \(-18\) \(0\) \(-114\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}+(-57+\cdots)q^{7}+\cdots\)
150.6.a.o \(2\) \(24.058\) \(\Q(\sqrt{1249}) \) None \(8\) \(18\) \(0\) \(114\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+6^{2}q^{6}+(57+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(150))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(150)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)