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Properties

Label 42.6
Level 42
Weight 6
Dimension 58
Nonzero newspaces 4
Newform subspaces 12
Sturm bound 576
Trace bound 4

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Defining parameters

Level: \( N \) = \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 12 \)
Sturm bound: \(576\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(42))\).

Total New Old
Modular forms 264 58 206
Cusp forms 216 58 158
Eisenstein series 48 0 48

Trace form

\( 58 q - 8 q^{2} + 32 q^{4} - 144 q^{6} - 640 q^{7} - 128 q^{8} + 570 q^{9} + O(q^{10}) \) \( 58 q - 8 q^{2} + 32 q^{4} - 144 q^{6} - 640 q^{7} - 128 q^{8} + 570 q^{9} + 2016 q^{10} + 1008 q^{11} - 3348 q^{13} - 704 q^{14} - 5220 q^{15} - 512 q^{16} + 4080 q^{17} + 840 q^{18} - 408 q^{19} + 2112 q^{20} + 6438 q^{21} + 480 q^{22} + 2628 q^{23} - 768 q^{24} - 19886 q^{25} + 7904 q^{26} + 8512 q^{28} + 5868 q^{29} + 11760 q^{30} + 6600 q^{31} - 2048 q^{32} - 37548 q^{33} - 24432 q^{34} - 11952 q^{35} + 12768 q^{36} - 41660 q^{37} - 5200 q^{38} + 39480 q^{39} + 32256 q^{40} + 54972 q^{41} + 63720 q^{42} + 64360 q^{43} + 16128 q^{44} + 5796 q^{45} - 97440 q^{46} - 93588 q^{47} - 13034 q^{49} - 101816 q^{50} - 110232 q^{51} - 15552 q^{52} + 49248 q^{53} - 54576 q^{54} - 53316 q^{55} + 30976 q^{56} + 97428 q^{57} + 82368 q^{58} + 127656 q^{59} + 42624 q^{60} + 195132 q^{61} - 110560 q^{62} + 119040 q^{63} - 90112 q^{64} + 97692 q^{65} + 160992 q^{66} - 14224 q^{67} + 65280 q^{68} - 103464 q^{69} - 64416 q^{70} - 129528 q^{71} - 34176 q^{72} - 509856 q^{73} - 212992 q^{74} - 486936 q^{75} - 97920 q^{76} + 140484 q^{77} + 51792 q^{78} + 687800 q^{79} - 138366 q^{81} + 102864 q^{82} + 390480 q^{83} + 95136 q^{84} + 409752 q^{85} + 111440 q^{86} + 575064 q^{87} + 122112 q^{88} + 27132 q^{89} - 54432 q^{90} - 203952 q^{91} - 196224 q^{92} - 1191096 q^{93} - 386688 q^{94} - 811788 q^{95} - 12288 q^{96} - 344808 q^{97} + 133336 q^{98} - 663624 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.6.a \(\chi_{42}(1, \cdot)\) 42.6.a.a 1 1
42.6.a.b 1
42.6.a.c 1
42.6.a.d 1
42.6.a.e 1
42.6.a.f 1
42.6.d \(\chi_{42}(41, \cdot)\) 42.6.d.a 12 1
42.6.e \(\chi_{42}(25, \cdot)\) 42.6.e.a 2 2
42.6.e.b 2
42.6.e.c 4
42.6.e.d 4
42.6.f \(\chi_{42}(5, \cdot)\) 42.6.f.a 28 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 1}\)