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Properties

Label 1150.3
Level 1150
Weight 3
Dimension 24240
Nonzero newspaces 12
Sturm bound 237600
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(237600\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1150))\).

Total New Old
Modular forms 80432 24240 56192
Cusp forms 77968 24240 53728
Eisenstein series 2464 0 2464

Trace form

\( 24240 q - 8 q^{2} - 16 q^{3} + 32 q^{6} + 16 q^{7} + 16 q^{8} + O(q^{10}) \) \( 24240 q - 8 q^{2} - 16 q^{3} + 32 q^{6} + 16 q^{7} + 16 q^{8} - 20 q^{10} - 64 q^{11} - 32 q^{12} + 24 q^{13} + 40 q^{15} - 32 q^{16} + 226 q^{17} + 132 q^{18} + 334 q^{19} + 80 q^{20} + 110 q^{21} + 224 q^{22} + 76 q^{23} - 220 q^{25} - 40 q^{26} - 190 q^{27} - 60 q^{28} - 246 q^{29} - 480 q^{30} + 54 q^{31} - 48 q^{32} - 350 q^{33} - 500 q^{34} - 400 q^{35} - 16 q^{36} - 256 q^{37} - 160 q^{38} + 536 q^{39} - 40 q^{40} + 168 q^{41} + 64 q^{42} + 56 q^{43} + 660 q^{45} + 16 q^{46} + 104 q^{47} + 64 q^{48} + 264 q^{49} + 100 q^{50} - 200 q^{51} + 48 q^{52} + 240 q^{53} - 308 q^{54} - 480 q^{55} - 200 q^{56} - 1158 q^{57} - 120 q^{58} - 684 q^{59} + 480 q^{60} - 440 q^{61} + 628 q^{62} + 514 q^{63} + 1580 q^{65} + 528 q^{66} + 1572 q^{67} + 608 q^{68} + 810 q^{69} + 560 q^{70} + 586 q^{71} + 192 q^{72} + 4 q^{73} + 528 q^{74} - 120 q^{75} + 160 q^{76} - 98 q^{77} - 44 q^{78} - 96 q^{79} + 152 q^{81} - 600 q^{82} - 922 q^{83} - 848 q^{84} - 920 q^{85} - 372 q^{86} - 2544 q^{87} - 128 q^{88} - 2944 q^{89} - 1940 q^{90} - 624 q^{91} - 376 q^{92} - 1112 q^{93} + 1592 q^{95} - 128 q^{96} + 7562 q^{97} + 4600 q^{98} + 12078 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1150))\)

We only show spaces with odd 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
1150.3.c \(\chi_{1150}(1149, \cdot)\) 1150.3.c.a 8 1
1150.3.c.b 32
1150.3.c.c 32
1150.3.d \(\chi_{1150}(551, \cdot)\) 1150.3.d.a 4 1
1150.3.d.b 16
1150.3.d.c 16
1150.3.d.d 16
1150.3.d.e 24
1150.3.f \(\chi_{1150}(93, \cdot)\) n/a 132 2
1150.3.h \(\chi_{1150}(91, \cdot)\) n/a 480 4
1150.3.j \(\chi_{1150}(229, \cdot)\) n/a 480 4
1150.3.l \(\chi_{1150}(47, \cdot)\) n/a 880 8
1150.3.n \(\chi_{1150}(51, \cdot)\) n/a 760 10
1150.3.o \(\chi_{1150}(99, \cdot)\) n/a 720 10
1150.3.q \(\chi_{1150}(193, \cdot)\) n/a 1440 20
1150.3.t \(\chi_{1150}(19, \cdot)\) n/a 4800 40
1150.3.v \(\chi_{1150}(11, \cdot)\) n/a 4800 40
1150.3.x \(\chi_{1150}(3, \cdot)\) n/a 9600 80

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1150))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1150)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 2}\)