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Properties

Label 300.6
Level 300
Weight 6
Dimension 4798
Nonzero newspaces 12
Sturm bound 28800
Trace bound 6

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(28800\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(300))\).

Total New Old
Modular forms 12280 4882 7398
Cusp forms 11720 4798 6922
Eisenstein series 560 84 476

Trace form

\( 4798 q - 4 q^{3} + 4 q^{4} + 38 q^{5} - 346 q^{6} + 168 q^{7} + 984 q^{8} + 296 q^{9} + O(q^{10}) \) \( 4798 q - 4 q^{3} + 4 q^{4} + 38 q^{5} - 346 q^{6} + 168 q^{7} + 984 q^{8} + 296 q^{9} + 1120 q^{10} + 80 q^{11} - 3258 q^{12} - 3160 q^{13} - 266 q^{15} + 10236 q^{16} + 11220 q^{17} - 4026 q^{18} - 4760 q^{19} - 6820 q^{20} - 1616 q^{21} - 6900 q^{22} + 5960 q^{23} + 22300 q^{24} + 4834 q^{25} + 23840 q^{26} - 2908 q^{27} - 1940 q^{28} + 11456 q^{29} - 23846 q^{30} - 12840 q^{31} + 51160 q^{32} + 12080 q^{33} + 12796 q^{34} + 37124 q^{35} + 5718 q^{36} - 100002 q^{37} - 157012 q^{38} + 7160 q^{39} + 65464 q^{40} + 11840 q^{41} + 120922 q^{42} + 131784 q^{43} + 103460 q^{44} - 258 q^{45} + 51140 q^{46} - 80080 q^{47} - 168356 q^{48} - 104078 q^{49} - 318364 q^{50} - 77780 q^{51} - 213592 q^{52} - 103378 q^{53} + 91352 q^{54} + 148408 q^{55} + 170440 q^{56} + 140884 q^{57} + 92216 q^{58} + 82816 q^{59} + 295314 q^{60} - 70808 q^{61} - 264828 q^{62} - 109186 q^{63} - 660320 q^{64} - 213390 q^{65} + 13310 q^{66} + 170568 q^{67} + 692512 q^{68} + 473818 q^{69} + 468708 q^{70} + 220800 q^{71} + 38750 q^{72} + 353784 q^{73} - 300162 q^{75} - 415976 q^{76} - 606816 q^{77} - 406872 q^{78} - 262768 q^{79} - 534404 q^{80} + 545960 q^{81} + 414188 q^{82} - 273320 q^{83} + 44614 q^{84} + 507274 q^{85} + 521960 q^{86} + 575190 q^{87} - 1359924 q^{88} + 2210290 q^{89} - 227650 q^{90} + 72960 q^{91} + 862328 q^{92} - 855386 q^{93} + 617564 q^{94} - 514480 q^{95} - 322798 q^{96} - 3572064 q^{97} - 243688 q^{98} + 102384 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.6.a \(\chi_{300}(1, \cdot)\) 300.6.a.a 1 1
300.6.a.b 1
300.6.a.c 1
300.6.a.d 1
300.6.a.e 1
300.6.a.f 1
300.6.a.g 2
300.6.a.h 2
300.6.a.i 3
300.6.a.j 3
300.6.d \(\chi_{300}(49, \cdot)\) 300.6.d.a 2 1
300.6.d.b 2
300.6.d.c 2
300.6.d.d 2
300.6.d.e 2
300.6.d.f 4
300.6.e \(\chi_{300}(251, \cdot)\) n/a 184 1
300.6.h \(\chi_{300}(299, \cdot)\) n/a 176 1
300.6.i \(\chi_{300}(257, \cdot)\) 300.6.i.a 4 2
300.6.i.b 4
300.6.i.c 8
300.6.i.d 20
300.6.i.e 24
300.6.j \(\chi_{300}(7, \cdot)\) n/a 180 2
300.6.m \(\chi_{300}(61, \cdot)\) 300.6.m.a 48 4
300.6.m.b 48
300.6.n \(\chi_{300}(11, \cdot)\) n/a 1184 4
300.6.o \(\chi_{300}(109, \cdot)\) n/a 104 4
300.6.r \(\chi_{300}(59, \cdot)\) n/a 1184 4
300.6.w \(\chi_{300}(67, \cdot)\) n/a 1200 8
300.6.x \(\chi_{300}(17, \cdot)\) n/a 400 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(300)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)