Properties

Label 26.4
Level 26
Weight 4
Dimension 21
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(26))\).

Total New Old
Modular forms 75 21 54
Cusp forms 51 21 30
Eisenstein series 24 0 24

Trace form

\( 21 q + 72 q^{7} + 24 q^{8} + O(q^{10}) \) \( 21 q + 72 q^{7} + 24 q^{8} - 90 q^{10} - 120 q^{11} - 48 q^{12} - 288 q^{13} - 120 q^{14} - 144 q^{15} + 237 q^{17} + 270 q^{18} + 684 q^{19} + 132 q^{20} + 120 q^{21} - 228 q^{23} - 375 q^{25} - 828 q^{27} + 288 q^{28} + 1053 q^{29} + 816 q^{30} + 564 q^{31} + 456 q^{33} - 432 q^{34} - 780 q^{35} - 768 q^{36} - 687 q^{37} - 1368 q^{38} - 1404 q^{39} - 1359 q^{41} - 936 q^{42} - 168 q^{43} - 192 q^{44} + 105 q^{45} + 432 q^{46} + 852 q^{47} + 1836 q^{49} + 2694 q^{50} + 4440 q^{51} + 852 q^{52} + 1044 q^{53} + 1656 q^{54} + 96 q^{56} - 564 q^{57} - 594 q^{58} - 1164 q^{59} - 1056 q^{60} - 663 q^{61} - 2088 q^{62} - 720 q^{63} - 192 q^{64} + 165 q^{65} - 2976 q^{66} - 1236 q^{67} - 156 q^{68} - 3876 q^{69} - 1224 q^{70} - 2208 q^{71} - 192 q^{72} - 1584 q^{73} + 2886 q^{74} + 2700 q^{75} + 2736 q^{76} + 2928 q^{77} + 5832 q^{78} + 3720 q^{79} + 528 q^{80} + 1872 q^{81} - 138 q^{82} - 4044 q^{83} - 1344 q^{84} - 4611 q^{85} - 1680 q^{86} - 4992 q^{87} - 960 q^{89} - 5400 q^{90} - 2160 q^{91} - 2112 q^{92} + 1668 q^{93} - 4680 q^{94} + 2136 q^{95} + 36 q^{97} + 4608 q^{98} + 5544 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)

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
26.4.a \(\chi_{26}(1, \cdot)\) 26.4.a.a 1 1
26.4.a.b 1
26.4.a.c 1
26.4.b \(\chi_{26}(25, \cdot)\) 26.4.b.a 4 1
26.4.c \(\chi_{26}(3, \cdot)\) 26.4.c.a 2 2
26.4.c.b 4
26.4.e \(\chi_{26}(17, \cdot)\) 26.4.e.a 8 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(26))\) into lower level spaces

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