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Properties

Label 150.6.g
Level $150$
Weight $6$
Character orbit 150.g
Rep. character $\chi_{150}(31,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $96$
Newform subspaces $4$
Sturm bound $180$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 150.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(150, [\chi])\).

Total New Old
Modular forms 616 96 520
Cusp forms 584 96 488
Eisenstein series 32 0 32

Trace form

\( 96 q - 8 q^{2} - 384 q^{4} + 66 q^{5} + 72 q^{6} - 548 q^{7} - 128 q^{8} - 1944 q^{9} + O(q^{10}) \) \( 96 q - 8 q^{2} - 384 q^{4} + 66 q^{5} + 72 q^{6} - 548 q^{7} - 128 q^{8} - 1944 q^{9} + 64 q^{10} + 948 q^{11} + 772 q^{13} - 594 q^{15} - 6144 q^{16} + 152 q^{17} + 2592 q^{18} + 6712 q^{19} - 704 q^{20} + 1764 q^{21} - 1408 q^{22} - 7236 q^{23} - 4608 q^{24} + 13624 q^{25} + 9552 q^{26} - 5728 q^{28} + 18348 q^{29} + 16704 q^{30} - 9966 q^{31} + 8192 q^{32} - 288 q^{33} + 24680 q^{34} - 48304 q^{35} - 31104 q^{36} - 23474 q^{37} - 1984 q^{38} + 1024 q^{40} + 5496 q^{41} - 26136 q^{42} + 84128 q^{43} - 10112 q^{44} + 5346 q^{45} + 37136 q^{46} - 39512 q^{47} + 139276 q^{49} + 7576 q^{50} - 41616 q^{51} + 12352 q^{52} + 62310 q^{53} + 5832 q^{54} - 18760 q^{55} + 23544 q^{57} - 10176 q^{58} + 93600 q^{59} + 6336 q^{60} + 127408 q^{61} - 175600 q^{62} + 51192 q^{63} - 98304 q^{64} - 138638 q^{65} + 34848 q^{66} + 184352 q^{67} + 63552 q^{68} + 108576 q^{69} - 536 q^{70} + 161128 q^{71} - 10368 q^{72} - 334848 q^{73} - 117232 q^{74} - 28296 q^{75} - 148608 q^{76} + 141776 q^{77} - 16704 q^{78} + 4236 q^{79} + 16896 q^{80} - 157464 q^{81} + 263216 q^{82} - 605608 q^{83} + 28224 q^{84} + 861566 q^{85} - 201696 q^{86} + 350496 q^{87} - 3968 q^{88} - 5334 q^{89} + 5184 q^{90} - 213428 q^{91} + 77184 q^{92} - 115056 q^{93} - 8448 q^{94} - 497584 q^{95} + 18432 q^{96} - 787294 q^{97} - 422344 q^{98} - 51192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.6.g.a 150.g 25.d $20$ $24.058$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(45\) \(-55\) \(180\) $\mathrm{SU}(2)[C_{5}]$ \(q-4\beta _{6}q^{2}-9\beta _{7}q^{3}+2^{4}\beta _{7}q^{4}+(-5+\cdots)q^{5}+\cdots\)
150.6.g.b 150.g 25.d $24$ $24.058$ None \(-24\) \(-54\) \(30\) \(-212\) $\mathrm{SU}(2)[C_{5}]$
150.6.g.c 150.g 25.d $24$ $24.058$ None \(24\) \(-54\) \(80\) \(-454\) $\mathrm{SU}(2)[C_{5}]$
150.6.g.d 150.g 25.d $28$ $24.058$ None \(-28\) \(63\) \(11\) \(-62\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{6}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)