Properties

Label 338.6
Level 338
Weight 6
Dimension 5845
Nonzero newspaces 8
Sturm bound 42588
Trace bound 1

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Defining parameters

Level: \( N \) = \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(42588\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(338))\).

Total New Old
Modular forms 17973 5845 12128
Cusp forms 17517 5845 11672
Eisenstein series 456 0 456

Trace form

\( 5845 q - 1192 q^{7} + 384 q^{8} + 2592 q^{9} + O(q^{10}) \) \( 5845 q - 1192 q^{7} + 384 q^{8} + 2592 q^{9} + 120 q^{10} - 2136 q^{11} - 1152 q^{12} - 3144 q^{13} - 1056 q^{14} + 4752 q^{15} + 2048 q^{16} + 1938 q^{17} + 9720 q^{18} + 10472 q^{19} - 3936 q^{20} - 264 q^{21} - 6456 q^{23} - 18750 q^{25} - 30312 q^{27} - 19072 q^{28} - 8190 q^{29} + 36672 q^{30} + 93104 q^{31} + 110040 q^{33} + 10560 q^{34} - 60720 q^{35} - 42240 q^{36} - 107230 q^{37} - 103968 q^{38} - 89076 q^{39} - 59166 q^{41} - 288 q^{42} + 116008 q^{43} + 72960 q^{44} + 308850 q^{45} + 125760 q^{46} + 185856 q^{47} + 27088 q^{49} - 147624 q^{50} - 634128 q^{51} - 45104 q^{52} + 33336 q^{53} + 236448 q^{54} + 241320 q^{55} + 84480 q^{56} + 340368 q^{57} + 86616 q^{58} + 112992 q^{59} - 46848 q^{60} + 33930 q^{61} - 224352 q^{62} - 811224 q^{63} - 24576 q^{64} - 94467 q^{65} - 343680 q^{66} - 144280 q^{67} - 9696 q^{68} + 280704 q^{69} + 98208 q^{70} + 271536 q^{71} + 218112 q^{72} + 16880 q^{73} + 22776 q^{74} - 48840 q^{75} + 167552 q^{76} + 85872 q^{77} + 214128 q^{78} + 323520 q^{79} - 62976 q^{80} - 551880 q^{81} + 280728 q^{82} + 303072 q^{83} + 40320 q^{84} + 90018 q^{85} - 169152 q^{86} + 55632 q^{87} + 113952 q^{89} - 972000 q^{90} - 253004 q^{91} - 354048 q^{92} - 401520 q^{93} - 549600 q^{94} - 1282128 q^{95} - 762568 q^{97} - 681984 q^{98} + 568872 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(338))\)

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
338.6.a \(\chi_{338}(1, \cdot)\) 338.6.a.a 1 1
338.6.a.b 1
338.6.a.c 1
338.6.a.d 1
338.6.a.e 1
338.6.a.f 2
338.6.a.g 2
338.6.a.h 3
338.6.a.i 3
338.6.a.j 4
338.6.a.k 4
338.6.a.l 6
338.6.a.m 6
338.6.a.n 6
338.6.a.o 6
338.6.a.p 9
338.6.a.q 9
338.6.b \(\chi_{338}(337, \cdot)\) 338.6.b.a 2 1
338.6.b.b 4
338.6.b.c 4
338.6.b.d 6
338.6.b.e 8
338.6.b.f 12
338.6.b.g 12
338.6.b.h 18
338.6.c \(\chi_{338}(191, \cdot)\) n/a 126 2
338.6.e \(\chi_{338}(23, \cdot)\) n/a 128 2
338.6.g \(\chi_{338}(27, \cdot)\) n/a 900 12
338.6.h \(\chi_{338}(25, \cdot)\) n/a 888 12
338.6.i \(\chi_{338}(3, \cdot)\) n/a 1848 24
338.6.k \(\chi_{338}(17, \cdot)\) n/a 1824 24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(338))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(338)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 1}\)