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Properties

Label 242.4
Level 242
Weight 4
Dimension 1785
Nonzero newspaces 4
Newform subspaces 39
Sturm bound 14520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 39 \)
Sturm bound: \(14520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(242))\).

Total New Old
Modular forms 5605 1785 3820
Cusp forms 5285 1785 3500
Eisenstein series 320 0 320

Trace form

\( 1785 q - 100 q^{6} - 40 q^{7} + 320 q^{9} + O(q^{10}) \) \( 1785 q - 100 q^{6} - 40 q^{7} + 320 q^{9} + 200 q^{10} + 100 q^{11} + 160 q^{12} + 80 q^{13} - 40 q^{14} - 820 q^{15} - 620 q^{17} - 460 q^{18} + 450 q^{19} + 840 q^{21} - 780 q^{23} - 400 q^{24} - 600 q^{25} - 400 q^{26} - 150 q^{27} + 240 q^{28} + 500 q^{29} + 1560 q^{30} - 180 q^{31} + 320 q^{32} + 1265 q^{33} + 1200 q^{34} + 2020 q^{35} + 200 q^{36} + 480 q^{37} + 120 q^{38} + 320 q^{39} - 480 q^{40} - 1660 q^{41} - 4360 q^{42} - 5380 q^{43} - 1060 q^{44} - 3820 q^{45} - 720 q^{46} + 500 q^{47} + 2660 q^{49} + 1360 q^{50} + 1390 q^{51} + 1920 q^{52} - 520 q^{53} + 4320 q^{54} + 370 q^{55} + 1890 q^{57} + 3360 q^{58} + 3650 q^{59} + 960 q^{60} - 520 q^{61} - 2760 q^{62} - 3440 q^{63} - 1520 q^{65} - 2920 q^{66} - 1640 q^{67} - 2480 q^{68} - 1680 q^{70} + 6480 q^{71} + 2240 q^{72} + 1740 q^{73} + 2800 q^{74} + 10090 q^{75} + 1520 q^{76} - 630 q^{77} + 5920 q^{78} - 480 q^{79} + 1280 q^{80} - 5010 q^{81} - 3380 q^{82} - 8890 q^{83} - 3680 q^{84} - 4840 q^{85} - 4900 q^{86} - 6800 q^{87} - 560 q^{88} - 700 q^{89} - 5880 q^{90} - 7660 q^{91} + 3360 q^{92} - 12460 q^{93} + 3200 q^{94} + 4400 q^{95} + 6690 q^{97} + 8820 q^{98} + 7790 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)

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
242.4.a \(\chi_{242}(1, \cdot)\) 242.4.a.a 1 1
242.4.a.b 1
242.4.a.c 1
242.4.a.d 1
242.4.a.e 1
242.4.a.f 1
242.4.a.g 1
242.4.a.h 2
242.4.a.i 2
242.4.a.j 2
242.4.a.k 2
242.4.a.l 2
242.4.a.m 2
242.4.a.n 4
242.4.a.o 4
242.4.c \(\chi_{242}(3, \cdot)\) 242.4.c.a 4 4
242.4.c.b 4
242.4.c.c 4
242.4.c.d 4
242.4.c.e 4
242.4.c.f 4
242.4.c.g 4
242.4.c.h 4
242.4.c.i 4
242.4.c.j 4
242.4.c.k 4
242.4.c.l 4
242.4.c.m 4
242.4.c.n 8
242.4.c.o 8
242.4.c.p 8
242.4.c.q 8
242.4.c.r 8
242.4.c.s 8
242.4.c.t 8
242.4.e \(\chi_{242}(23, \cdot)\) 242.4.e.a 160 10
242.4.e.b 170
242.4.g \(\chi_{242}(5, \cdot)\) 242.4.g.a 640 40
242.4.g.b 680

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)