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Properties

Label 150.4.h
Level $150$
Weight $4$
Character orbit 150.h
Rep. character $\chi_{150}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $56$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 150.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 376 56 320
Cusp forms 344 56 288
Eisenstein series 32 0 32

Trace form

\( 56 q + 56 q^{4} - 4 q^{5} + 12 q^{6} + 126 q^{9} + O(q^{10}) \) \( 56 q + 56 q^{4} - 4 q^{5} + 12 q^{6} + 126 q^{9} + 44 q^{10} + 168 q^{11} + 66 q^{15} - 224 q^{16} - 640 q^{17} - 148 q^{19} + 256 q^{20} + 84 q^{21} + 360 q^{22} + 740 q^{23} + 192 q^{24} + 714 q^{25} - 368 q^{26} + 120 q^{28} + 368 q^{29} - 96 q^{30} + 414 q^{31} - 960 q^{33} - 440 q^{34} - 1764 q^{35} - 504 q^{36} - 700 q^{37} - 176 q^{40} - 464 q^{41} + 1020 q^{42} + 448 q^{44} + 36 q^{45} + 1016 q^{46} + 1720 q^{47} - 1164 q^{49} + 176 q^{50} - 816 q^{51} + 5100 q^{53} - 108 q^{54} - 2280 q^{55} - 1800 q^{59} + 576 q^{60} - 692 q^{61} - 3480 q^{62} + 360 q^{63} + 896 q^{64} - 2448 q^{65} + 528 q^{66} + 720 q^{67} + 696 q^{69} + 2084 q^{70} + 2168 q^{71} + 600 q^{73} - 752 q^{74} + 264 q^{75} - 1408 q^{76} - 2240 q^{77} + 3716 q^{79} - 64 q^{80} - 1134 q^{81} - 8380 q^{83} - 336 q^{84} + 1856 q^{85} - 336 q^{86} - 1140 q^{87} + 1680 q^{88} + 936 q^{89} - 396 q^{90} - 5008 q^{91} - 1408 q^{94} + 11016 q^{95} + 192 q^{96} - 4350 q^{97} - 6560 q^{98} + 1008 q^{99} + O(q^{100}) \)

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.h.a 150.h 25.e $24$ $8.850$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
150.4.h.b 150.h 25.e $32$ $8.850$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

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