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Properties

Label 42.5
Level 42
Weight 5
Dimension 44
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(42))\).

Total New Old
Modular forms 216 44 172
Cusp forms 168 44 124
Eisenstein series 48 0 48

Trace form

\( 44 q + 30 q^{3} - 108 q^{5} - 96 q^{6} + 156 q^{7} + 258 q^{9} + O(q^{10}) \) \( 44 q + 30 q^{3} - 108 q^{5} - 96 q^{6} + 156 q^{7} + 258 q^{9} + 384 q^{10} - 612 q^{11} - 240 q^{12} - 844 q^{13} + 348 q^{15} - 256 q^{16} + 864 q^{17} + 1344 q^{18} + 2408 q^{19} - 1710 q^{21} - 1344 q^{22} - 1440 q^{23} + 896 q^{25} + 1152 q^{26} - 3744 q^{27} - 1024 q^{28} - 3960 q^{29} - 1344 q^{30} + 2096 q^{31} + 3354 q^{33} + 2304 q^{34} + 3060 q^{35} - 3840 q^{36} + 6756 q^{37} + 8640 q^{38} + 10008 q^{39} - 3072 q^{40} - 1824 q^{42} - 14952 q^{43} - 4896 q^{44} - 12102 q^{45} - 9600 q^{46} - 13932 q^{47} + 768 q^{48} - 2632 q^{49} + 9216 q^{50} - 4338 q^{51} + 3488 q^{52} + 7272 q^{53} + 10656 q^{54} + 47376 q^{55} + 4608 q^{56} + 21660 q^{57} + 1920 q^{58} - 5112 q^{59} + 7056 q^{60} + 2672 q^{61} + 1878 q^{63} - 6144 q^{64} - 16380 q^{65} - 14784 q^{66} - 32144 q^{67} - 6912 q^{68} - 59796 q^{69} - 41856 q^{70} - 21456 q^{71} - 10752 q^{72} + 8828 q^{73} + 13824 q^{74} + 48852 q^{75} + 5792 q^{76} + 38448 q^{77} + 19968 q^{78} + 11848 q^{79} + 6912 q^{80} + 45858 q^{81} + 7296 q^{82} - 2352 q^{84} - 47928 q^{85} + 10944 q^{86} - 31896 q^{87} + 15360 q^{88} - 27576 q^{89} - 22848 q^{90} - 37432 q^{91} + 8640 q^{92} - 26418 q^{93} - 7296 q^{94} - 17244 q^{95} + 75104 q^{97} + 25344 q^{98} + 84252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.5.b \(\chi_{42}(29, \cdot)\) 42.5.b.a 8 1
42.5.c \(\chi_{42}(13, \cdot)\) 42.5.c.a 4 1
42.5.g \(\chi_{42}(19, \cdot)\) 42.5.g.a 4 2
42.5.g.b 8
42.5.h \(\chi_{42}(11, \cdot)\) 42.5.h.a 20 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)