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Properties

Label 10.13
Level 10
Weight 13
Dimension 12
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 78
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(78\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(10))\).

Total New Old
Modular forms 40 12 28
Cusp forms 32 12 20
Eisenstein series 8 0 8

Trace form

\( 12 q - 640 q^{3} - 1800 q^{5} + 78848 q^{6} - 367440 q^{7} + O(q^{10}) \) \( 12 q - 640 q^{3} - 1800 q^{5} + 78848 q^{6} - 367440 q^{7} + 867840 q^{10} - 1765296 q^{11} - 1310720 q^{12} + 3460020 q^{13} - 15082480 q^{15} - 50331648 q^{16} + 61972740 q^{17} + 27822080 q^{18} - 54190080 q^{20} - 55913296 q^{21} + 162263040 q^{22} + 346973760 q^{23} - 682458300 q^{25} - 816233472 q^{26} + 2064641360 q^{27} + 752517120 q^{28} - 2464435200 q^{30} - 4376225376 q^{31} + 10797394640 q^{33} - 11582581680 q^{35} + 2894667776 q^{36} + 1005341340 q^{37} + 1802695680 q^{38} - 2249195520 q^{40} - 2026801296 q^{41} + 9285114880 q^{42} - 1357559520 q^{43} + 8988051460 q^{45} - 8660477952 q^{46} - 10068243840 q^{47} + 2684354560 q^{48} + 12452428800 q^{50} + 31168538464 q^{51} + 7086120960 q^{52} - 86723398980 q^{53} + 113239460400 q^{55} + 36276535296 q^{56} - 144146964640 q^{57} - 107285130240 q^{58} + 99082895360 q^{60} + 90518069424 q^{61} - 30656286720 q^{62} - 147686550400 q^{63} + 173117966220 q^{65} - 130203817984 q^{66} + 104416726080 q^{67} - 126920171520 q^{68} + 21297884160 q^{70} + 358733348064 q^{71} + 56979619840 q^{72} + 722920298220 q^{73} - 1108294984400 q^{75} - 387391979520 q^{76} - 427325430960 q^{77} + 342313912320 q^{78} + 7549747200 q^{80} + 78995180452 q^{81} + 1519071928320 q^{82} + 796544103600 q^{83} - 1316786650380 q^{85} - 1947103368192 q^{86} - 333007377280 q^{87} - 332314705920 q^{88} + 1253888330240 q^{90} + 222319671744 q^{91} + 710602260480 q^{92} + 2824159805360 q^{93} - 2482880641200 q^{95} - 330712481792 q^{96} - 1532104852500 q^{97} - 3288563527680 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.13.c \(\chi_{10}(3, \cdot)\) 10.13.c.a 6 2
10.13.c.b 6

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)