Properties

Label 150.3.f
Level $150$
Weight $3$
Character orbit 150.f
Rep. character $\chi_{150}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $3$
Sturm bound $90$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(90\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(150, [\chi])\).

Total New Old
Modular forms 144 12 132
Cusp forms 96 12 84
Eisenstein series 48 0 48

Trace form

\( 12q - 4q^{2} + 16q^{7} + 8q^{8} + O(q^{10}) \) \( 12q - 4q^{2} + 16q^{7} + 8q^{8} + 32q^{11} - 12q^{13} - 48q^{16} - 44q^{17} - 12q^{18} + 24q^{21} + 16q^{22} + 16q^{23} - 168q^{26} - 32q^{28} - 120q^{31} + 16q^{32} + 48q^{33} + 72q^{36} + 108q^{37} + 64q^{38} + 416q^{41} - 48q^{42} - 48q^{43} + 64q^{46} - 96q^{47} - 96q^{51} - 24q^{52} - 100q^{53} - 128q^{56} - 48q^{57} - 64q^{58} - 8q^{61} + 80q^{62} + 48q^{63} + 192q^{66} + 16q^{67} + 88q^{68} - 128q^{71} - 24q^{72} + 188q^{73} + 176q^{76} + 128q^{77} - 96q^{78} - 108q^{81} - 32q^{82} - 192q^{83} - 192q^{86} + 48q^{87} - 32q^{88} - 936q^{91} + 32q^{92} + 96q^{93} - 132q^{97} + 124q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
150.3.f.a \(4\) \(4.087\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(-24\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
150.3.f.b \(4\) \(4.087\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(16\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
150.3.f.c \(4\) \(4.087\) \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(24\) \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)