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Properties

Label 150.4
Level 150
Weight 4
Dimension 415
Nonzero newspaces 6
Newform subspaces 25
Sturm bound 4800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 25 \)
Sturm bound: \(4800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(150))\).

Total New Old
Modular forms 1912 415 1497
Cusp forms 1688 415 1273
Eisenstein series 224 0 224

Trace form

\( 415 q + 6 q^{2} - 19 q^{3} - 12 q^{4} - 10 q^{5} - 10 q^{6} - 32 q^{7} + 24 q^{8} - 27 q^{9} + O(q^{10}) \) \( 415 q + 6 q^{2} - 19 q^{3} - 12 q^{4} - 10 q^{5} - 10 q^{6} - 32 q^{7} + 24 q^{8} - 27 q^{9} + 52 q^{10} - 100 q^{11} + 52 q^{12} + 190 q^{13} + 32 q^{14} + 256 q^{15} + 208 q^{16} - 758 q^{17} - 94 q^{18} - 572 q^{19} + 32 q^{20} - 784 q^{21} + 840 q^{22} + 1112 q^{23} + 312 q^{24} + 2774 q^{25} + 532 q^{26} + 1349 q^{27} + 352 q^{28} + 662 q^{29} - 360 q^{30} - 1080 q^{31} - 224 q^{32} - 2740 q^{33} - 3608 q^{34} - 3568 q^{35} - 1132 q^{36} - 2968 q^{37} - 744 q^{38} - 2554 q^{39} + 144 q^{40} - 294 q^{41} + 2464 q^{42} + 6012 q^{43} + 1840 q^{44} + 3630 q^{45} + 3824 q^{46} + 4016 q^{47} + 208 q^{48} + 2607 q^{49} - 252 q^{50} + 1342 q^{51} - 1160 q^{52} + 2448 q^{53} - 378 q^{54} - 344 q^{55} + 256 q^{56} - 2700 q^{57} - 5196 q^{58} - 4580 q^{59} + 1632 q^{60} - 2826 q^{61} - 2544 q^{62} - 2128 q^{63} - 192 q^{64} - 3146 q^{65} - 688 q^{66} - 1964 q^{67} + 2088 q^{68} - 3880 q^{69} + 2688 q^{70} + 1080 q^{71} + 88 q^{72} - 1550 q^{73} + 1364 q^{74} - 11256 q^{75} + 1168 q^{76} + 4032 q^{77} + 844 q^{78} + 5704 q^{79} - 160 q^{80} + 5181 q^{81} - 2436 q^{82} - 3140 q^{83} - 192 q^{84} - 4186 q^{85} - 3224 q^{86} - 2346 q^{87} - 2400 q^{88} - 5356 q^{89} + 4684 q^{90} - 1552 q^{91} - 2592 q^{92} + 5440 q^{93} - 5440 q^{94} + 7376 q^{95} + 352 q^{96} + 18130 q^{97} + 3510 q^{98} + 4140 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
150.4.a \(\chi_{150}(1, \cdot)\) 150.4.a.a 1 1
150.4.a.b 1
150.4.a.c 1
150.4.a.d 1
150.4.a.e 1
150.4.a.f 1
150.4.a.g 1
150.4.a.h 1
150.4.a.i 1
150.4.c \(\chi_{150}(49, \cdot)\) 150.4.c.a 2 1
150.4.c.b 2
150.4.c.c 2
150.4.c.d 2
150.4.c.e 2
150.4.e \(\chi_{150}(107, \cdot)\) 150.4.e.a 4 2
150.4.e.b 4
150.4.e.c 12
150.4.e.d 16
150.4.g \(\chi_{150}(31, \cdot)\) 150.4.g.a 12 4
150.4.g.b 16
150.4.g.c 16
150.4.g.d 20
150.4.h \(\chi_{150}(19, \cdot)\) 150.4.h.a 24 4
150.4.h.b 32
150.4.l \(\chi_{150}(17, \cdot)\) 150.4.l.a 240 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)