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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(150))\) 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 3 5
150.6.a.a 150.a 1.a $1$ $24.058$ \(\Q\) None \(-4\) \(-9\) \(0\) \(-47\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}-47q^{7}+\cdots\)
150.6.a.b 150.a 1.a $1$ $24.058$ \(\Q\) None \(-4\) \(-9\) \(0\) \(-32\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}-2^{5}q^{7}+\cdots\)
150.6.a.c 150.a 1.a $1$ $24.058$ \(\Q\) None \(-4\) \(-9\) \(0\) \(233\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}+233q^{7}+\cdots\)
150.6.a.d 150.a 1.a $1$ $24.058$ \(\Q\) None \(-4\) \(9\) \(0\) \(-176\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}-176q^{7}+\cdots\)
150.6.a.e 150.a 1.a $1$ $24.058$ \(\Q\) None \(-4\) \(9\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}-q^{7}+\cdots\)
150.6.a.f 150.a 1.a $1$ $24.058$ \(\Q\) None \(-4\) \(9\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}+4q^{7}+\cdots\)
150.6.a.g 150.a 1.a $1$ $24.058$ \(\Q\) None \(-4\) \(9\) \(0\) \(79\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}+79q^{7}+\cdots\)
150.6.a.h 150.a 1.a $1$ $24.058$ \(\Q\) None \(4\) \(-9\) \(0\) \(-164\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}-164q^{7}+\cdots\)
150.6.a.i 150.a 1.a $1$ $24.058$ \(\Q\) None \(4\) \(-9\) \(0\) \(-79\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}-79q^{7}+\cdots\)
150.6.a.j 150.a 1.a $1$ $24.058$ \(\Q\) None \(4\) \(-9\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}-4q^{7}+\cdots\)
150.6.a.k 150.a 1.a $1$ $24.058$ \(\Q\) None \(4\) \(-9\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6^{2}q^{6}+q^{7}+\cdots\)
150.6.a.l 150.a 1.a $1$ $24.058$ \(\Q\) None \(4\) \(9\) \(0\) \(-233\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+6^{2}q^{6}-233q^{7}+\cdots\)
150.6.a.m 150.a 1.a $1$ $24.058$ \(\Q\) None \(4\) \(9\) \(0\) \(47\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+6^{2}q^{6}+47q^{7}+\cdots\)
150.6.a.n 150.a 1.a $2$ $24.058$ \(\Q(\sqrt{1249}) \) None \(-8\) \(-18\) \(0\) \(-114\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}+(-57+\cdots)q^{7}+\cdots\)
150.6.a.o 150.a 1.a $2$ $24.058$ \(\Q(\sqrt{1249}) \) None \(8\) \(18\) \(0\) \(114\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+6^{2}q^{6}+(57+\cdots)q^{7}+\cdots\)

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

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