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Properties

Label 10.10
Level 10
Weight 10
Dimension 7
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(10))\).

Total New Old
Modular forms 31 7 24
Cusp forms 23 7 16
Eisenstein series 8 0 8

Trace form

\( 7 q - 16 q^{2} + 16 q^{3} - 256 q^{4} - 3205 q^{5} + 448 q^{6} - 228 q^{7} - 4096 q^{8} - 57013 q^{9} + O(q^{10}) \) \( 7 q - 16 q^{2} + 16 q^{3} - 256 q^{4} - 3205 q^{5} + 448 q^{6} - 228 q^{7} - 4096 q^{8} - 57013 q^{9} + 45040 q^{10} - 6276 q^{11} + 4096 q^{12} - 232974 q^{13} + 337792 q^{14} + 379240 q^{15} + 458752 q^{16} - 934458 q^{17} + 99632 q^{18} + 1689660 q^{19} + 500480 q^{20} - 5379896 q^{21} - 629952 q^{22} + 2695956 q^{23} + 2605056 q^{24} + 770775 q^{25} - 7416032 q^{26} - 3754160 q^{27} - 58368 q^{28} + 10515330 q^{29} - 4269120 q^{30} + 15017464 q^{31} - 1048576 q^{32} - 10293648 q^{33} - 7060768 q^{34} + 13444420 q^{35} + 22254336 q^{36} + 28529802 q^{37} - 31419200 q^{38} - 59400976 q^{39} - 16650240 q^{40} + 20113374 q^{41} + 38291968 q^{42} - 39518424 q^{43} + 51452928 q^{44} - 13091985 q^{45} + 6640768 q^{46} - 27549708 q^{47} + 1048576 q^{48} - 71368737 q^{49} - 28253200 q^{50} - 122250496 q^{51} - 59641344 q^{52} + 181541706 q^{53} + 311556480 q^{54} + 237238940 q^{55} - 8290304 q^{56} - 239106400 q^{57} - 180687840 q^{58} + 287111460 q^{59} - 232765440 q^{60} - 395018086 q^{61} + 142425088 q^{62} + 349738556 q^{63} - 16777216 q^{64} + 403570090 q^{65} - 103172864 q^{66} - 56692488 q^{67} - 239221248 q^{68} - 1240048136 q^{69} - 674616960 q^{70} + 829596144 q^{71} + 25505792 q^{72} + 283392846 q^{73} + 968831392 q^{74} + 285810800 q^{75} + 269982720 q^{76} + 594093984 q^{77} - 865437056 q^{78} - 2219911200 q^{79} - 210042880 q^{80} + 721923927 q^{81} + 733577568 q^{82} + 560234736 q^{83} + 981854208 q^{84} + 731884670 q^{85} + 1316223808 q^{86} - 845703360 q^{87} - 161267712 q^{88} - 1226641290 q^{89} - 2422234320 q^{90} - 2017529736 q^{91} + 690164736 q^{92} + 2509309712 q^{93} + 2064301312 q^{94} + 528928300 q^{95} + 29360128 q^{96} - 961141338 q^{97} - 1182674832 q^{98} - 1384367956 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.10.a \(\chi_{10}(1, \cdot)\) 10.10.a.a 1 1
10.10.a.b 1
10.10.a.c 1
10.10.b \(\chi_{10}(9, \cdot)\) 10.10.b.a 4 1

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)