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Properties

Label 150.3.d
Level $150$
Weight $3$
Character orbit 150.d
Rep. character $\chi_{150}(101,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $90$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(90\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 72 12 60
Cusp forms 48 12 36
Eisenstein series 24 0 24

Trace form

\( 12 q - 4 q^{3} - 24 q^{4} + 8 q^{6} - 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{3} - 24 q^{4} + 8 q^{6} - 8 q^{7} - 4 q^{9} + 8 q^{12} + 40 q^{13} + 48 q^{16} - 32 q^{18} - 44 q^{19} + 44 q^{21} - 48 q^{22} - 16 q^{24} - 28 q^{27} + 16 q^{28} - 124 q^{31} - 24 q^{33} + 112 q^{34} + 8 q^{36} + 88 q^{37} + 60 q^{39} + 128 q^{42} - 56 q^{43} - 32 q^{46} - 16 q^{48} + 120 q^{49} - 184 q^{51} - 80 q^{52} - 40 q^{54} - 152 q^{57} - 132 q^{61} + 256 q^{63} - 96 q^{64} - 176 q^{66} + 328 q^{67} + 224 q^{69} + 64 q^{72} - 200 q^{73} + 88 q^{76} - 40 q^{78} - 56 q^{79} + 284 q^{81} - 192 q^{82} - 88 q^{84} - 240 q^{87} + 96 q^{88} + 620 q^{91} - 32 q^{93} + 80 q^{94} + 32 q^{96} - 296 q^{97} - 656 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.3.d.a 150.d 3.b $2$ $4.087$ \(\Q(\sqrt{-2}) \) None 150.3.d.a \(0\) \(-2\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}+(4-\beta )q^{6}+\cdots\)
150.3.d.b 150.d 3.b $2$ $4.087$ \(\Q(\sqrt{-2}) \) None 150.3.d.a \(0\) \(2\) \(0\) \(14\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(1-2\beta )q^{3}-2q^{4}+(4+\beta )q^{6}+\cdots\)
150.3.d.c 150.d 3.b $4$ $4.087$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None 30.3.d.a \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}-2q^{4}+\cdots\)
150.3.d.d 150.d 3.b $4$ $4.087$ \(\Q(\sqrt{-2}, \sqrt{-17})\) None 30.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}+(-1+\beta _{3})q^{6}+\cdots\)

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

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