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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.3.f.a 150.f 5.c $4$ $4.087$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
150.3.f.b 150.f 5.c $4$ $4.087$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
150.3.f.c 150.f 5.c $4$ $4.087$ \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)

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

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