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Properties

Label 150.3.k
Level $150$
Weight $3$
Character orbit 150.k
Rep. character $\chi_{150}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $80$
Newform subspaces $2$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.k (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 512 80 432
Cusp forms 448 80 368
Eisenstein series 64 0 64

Trace form

\( 80 q - 4 q^{2} + 16 q^{7} + 8 q^{8} + O(q^{10}) \) \( 80 q - 4 q^{2} + 16 q^{7} + 8 q^{8} - 4 q^{10} - 12 q^{13} + 24 q^{15} + 80 q^{16} + 236 q^{17} + 48 q^{18} + 200 q^{19} + 32 q^{20} + 96 q^{22} + 96 q^{23} - 92 q^{25} + 40 q^{26} - 112 q^{28} - 400 q^{29} - 192 q^{30} - 64 q^{32} - 312 q^{33} - 100 q^{34} - 328 q^{35} - 120 q^{36} + 228 q^{37} + 64 q^{38} - 8 q^{40} - 160 q^{41} - 48 q^{42} + 432 q^{43} + 12 q^{45} + 64 q^{47} - 92 q^{50} - 24 q^{52} - 460 q^{53} - 672 q^{55} - 48 q^{57} - 64 q^{58} - 800 q^{59} + 48 q^{60} + 240 q^{61} + 80 q^{62} + 48 q^{63} + 44 q^{65} + 576 q^{67} + 88 q^{68} + 352 q^{70} - 24 q^{72} + 268 q^{73} - 48 q^{75} + 128 q^{77} - 96 q^{78} - 400 q^{79} + 180 q^{81} - 672 q^{82} + 448 q^{83} - 688 q^{85} + 528 q^{87} - 32 q^{88} + 100 q^{89} + 12 q^{90} + 32 q^{92} + 336 q^{93} + 256 q^{95} - 92 q^{97} + 124 q^{98} + O(q^{100}) \)

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.k.a 150.k 25.f $32$ $4.087$ None \(8\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{20}]$
150.3.k.b 150.k 25.f $48$ $4.087$ None \(-12\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{20}]$

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

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