Properties

Label 150.4.a
Level $150$
Weight $4$
Character orbit 150.a
Rep. character $\chi_{150}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $9$
Sturm bound $120$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(120\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(150))\).

Total New Old
Modular forms 102 9 93
Cusp forms 78 9 69
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.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
Plus space\(+\)\(6\)
Minus space\(-\)\(3\)

Trace form

\( 9q + 2q^{2} - 3q^{3} + 36q^{4} - 6q^{6} - 12q^{7} + 8q^{8} + 81q^{9} + O(q^{10}) \) \( 9q + 2q^{2} - 3q^{3} + 36q^{4} - 6q^{6} - 12q^{7} + 8q^{8} + 81q^{9} + 68q^{11} - 12q^{12} - 6q^{13} + 48q^{14} + 144q^{16} + 198q^{17} + 18q^{18} + 200q^{19} + 12q^{21} - 240q^{23} - 24q^{24} + 596q^{26} - 27q^{27} - 48q^{28} - 210q^{29} - 452q^{31} + 32q^{32} + 360q^{33} - 52q^{34} + 324q^{36} - 54q^{37} - 392q^{38} - 306q^{39} - 622q^{41} + 312q^{42} + 732q^{43} + 272q^{44} + 656q^{46} + 240q^{47} - 48q^{48} - 723q^{49} - 498q^{51} - 24q^{52} - 342q^{53} - 54q^{54} + 192q^{56} - 132q^{57} - 348q^{58} + 340q^{59} - 2742q^{61} - 1184q^{62} - 108q^{63} + 576q^{64} + 168q^{66} - 2292q^{67} + 792q^{68} + 384q^{69} - 72q^{71} + 72q^{72} - 486q^{73} - 732q^{74} + 800q^{76} + 1920q^{77} - 444q^{78} + 2240q^{79} + 729q^{81} + 948q^{82} + 1644q^{83} + 48q^{84} - 1224q^{86} - 558q^{87} - 4990q^{89} - 452q^{91} - 960q^{92} - 384q^{93} - 1472q^{94} - 96q^{96} + 186q^{97} + 1842q^{98} + 612q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(150))\) 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
150.4.a.a \(1\) \(8.850\) \(\Q\) None \(-2\) \(-3\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-q^{7}+\cdots\)
150.4.a.b \(1\) \(8.850\) \(\Q\) None \(-2\) \(-3\) \(0\) \(4\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+4q^{7}+\cdots\)
150.4.a.c \(1\) \(8.850\) \(\Q\) None \(-2\) \(3\) \(0\) \(-23\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-23q^{7}+\cdots\)
150.4.a.d \(1\) \(8.850\) \(\Q\) None \(-2\) \(3\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+2q^{7}+\cdots\)
150.4.a.e \(1\) \(8.850\) \(\Q\) None \(2\) \(-3\) \(0\) \(-32\) \(-\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2^{5}q^{7}+\cdots\)
150.4.a.f \(1\) \(8.850\) \(\Q\) None \(2\) \(-3\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2q^{7}+\cdots\)
150.4.a.g \(1\) \(8.850\) \(\Q\) None \(2\) \(-3\) \(0\) \(23\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+23q^{7}+\cdots\)
150.4.a.h \(1\) \(8.850\) \(\Q\) None \(2\) \(3\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+q^{7}+\cdots\)
150.4.a.i \(1\) \(8.850\) \(\Q\) None \(2\) \(3\) \(0\) \(16\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+2^{4}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(150))\) into lower level spaces

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