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Properties

Label 150.4.l
Level $150$
Weight $4$
Character orbit 150.l
Rep. character $\chi_{150}(17,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 150.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(150, [\chi])\).

Total New Old
Modular forms 752 240 512
Cusp forms 688 240 448
Eisenstein series 64 0 64

Trace form

\( 240 q - 8 q^{3} - 12 q^{7} + O(q^{10}) \) \( 240 q - 8 q^{3} - 12 q^{7} - 24 q^{10} + 32 q^{12} + 120 q^{13} + 172 q^{15} + 960 q^{16} + 16 q^{18} - 240 q^{19} + 408 q^{22} + 2376 q^{25} + 688 q^{27} + 192 q^{28} - 168 q^{30} - 788 q^{33} - 2640 q^{34} - 768 q^{37} - 2440 q^{39} + 192 q^{40} + 872 q^{42} + 1968 q^{43} + 3648 q^{45} + 128 q^{48} - 480 q^{52} - 1572 q^{55} - 1528 q^{57} - 2280 q^{58} + 1824 q^{60} - 788 q^{63} + 312 q^{67} - 6160 q^{69} - 1704 q^{70} - 64 q^{72} - 5940 q^{73} - 10728 q^{75} - 2120 q^{78} - 4320 q^{79} + 1280 q^{81} - 3648 q^{82} + 960 q^{84} + 312 q^{85} + 4580 q^{87} - 1248 q^{88} + 4792 q^{90} + 4776 q^{93} + 9456 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.4.l.a 150.l 75.l $240$ $8.850$ None \(0\) \(-8\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{4}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

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