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Properties

Label 12.13
Level 12
Weight 13
Dimension 16
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 104
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(104\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(12))\).

Total New Old
Modular forms 53 16 37
Cusp forms 43 16 27
Eisenstein series 10 0 10

Trace form

\( 16 q - 90 q^{2} + 300 q^{3} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} + 15800 q^{7} - 648000 q^{8} - 2028960 q^{9} + O(q^{10}) \) \( 16 q - 90 q^{2} + 300 q^{3} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} + 15800 q^{7} - 648000 q^{8} - 2028960 q^{9} + 923028 q^{10} - 3018060 q^{12} + 5527040 q^{13} + 15389208 q^{14} + 6613920 q^{15} - 61526928 q^{16} - 12097800 q^{17} + 15943230 q^{18} - 2050024 q^{19} - 377644248 q^{20} - 15078504 q^{21} + 482545560 q^{22} - 332039088 q^{24} + 621296872 q^{25} + 243358236 q^{26} + 508358700 q^{27} - 185369520 q^{28} + 1997608680 q^{29} - 577761660 q^{30} - 2519008264 q^{31} + 1733536800 q^{32} + 4117286160 q^{33} - 7816269348 q^{34} + 831173724 q^{36} - 8426882080 q^{37} - 8280525240 q^{38} + 14132878296 q^{39} + 3985807104 q^{40} + 5806392696 q^{41} - 1390844520 q^{42} - 26119930600 q^{43} + 4989496464 q^{44} + 37700632872 q^{45} + 4149450240 q^{46} - 7791843600 q^{48} - 112606916328 q^{49} + 68552901522 q^{50} + 54522702720 q^{51} - 31090133640 q^{52} + 42482511720 q^{53} + 8523250758 q^{54} - 96029271360 q^{55} - 38053468224 q^{56} + 10609651320 q^{57} + 159666562500 q^{58} - 19968517224 q^{60} + 128061332384 q^{61} - 27876030840 q^{62} + 18020676600 q^{63} + 188355529344 q^{64} - 328250713392 q^{65} - 136719325224 q^{66} + 89055584600 q^{67} + 77938316280 q^{68} + 70973432064 q^{69} - 454939318704 q^{70} + 114791256000 q^{72} - 340335405280 q^{73} - 502785766548 q^{74} - 487877005140 q^{75} + 143972453808 q^{76} + 1383727360320 q^{77} - 72052158420 q^{78} + 567022026488 q^{79} - 417712547808 q^{80} - 552478803408 q^{81} + 460673773020 q^{82} + 28008331632 q^{84} + 2453414203344 q^{85} + 1255416205464 q^{86} - 976838637600 q^{87} + 47622991680 q^{88} - 1422946205928 q^{89} - 163511641116 q^{90} + 762832207984 q^{91} - 3462722444160 q^{92} - 336005568840 q^{93} + 847910842896 q^{94} + 341032101984 q^{96} - 3193715332000 q^{97} + 1702751294790 q^{98} + 1272066016320 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.13.c \(\chi_{12}(5, \cdot)\) 12.13.c.a 4 1
12.13.d \(\chi_{12}(7, \cdot)\) 12.13.d.a 12 1

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)