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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
150.6.g.a \(20\) \(24.058\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(45\) \(-55\) \(180\) \(q-4\beta _{6}q^{2}-9\beta _{7}q^{3}+2^{4}\beta _{7}q^{4}+(-5+\cdots)q^{5}+\cdots\)
150.6.g.b \(24\) \(24.058\) None \(-24\) \(-54\) \(30\) \(-212\)
150.6.g.c \(24\) \(24.058\) None \(24\) \(-54\) \(80\) \(-454\)
150.6.g.d \(28\) \(24.058\) None \(-28\) \(63\) \(11\) \(-62\)

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

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