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Properties

Label 12.17
Level 12
Weight 17
Dimension 21
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 136
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(136\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(12))\).

Total New Old
Modular forms 69 21 48
Cusp forms 59 21 38
Eisenstein series 10 0 10

Trace form

\( 21 q - 186 q^{2} - 5859 q^{3} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 3693274 q^{7} + 14683680 q^{8} - 196657227 q^{9} + O(q^{10}) \) \( 21 q - 186 q^{2} - 5859 q^{3} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 3693274 q^{7} + 14683680 q^{8} - 196657227 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 1530674262 q^{13} - 806064072 q^{14} - 1065273120 q^{15} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} - 8480173190 q^{19} + 1002788712 q^{20} + 15328543626 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} - 166669683403 q^{25} + 1054507182588 q^{26} - 174996691299 q^{27} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 144168489830 q^{31} - 5158730488416 q^{32} + 678638230560 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 9662248568790 q^{37} + 23318999782920 q^{38} + 6868972574010 q^{39} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} + 7789188108154 q^{43} - 11442227373552 q^{44} + 25705208790432 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 155092532412065 q^{49} - 133601044957998 q^{50} + 65388537498240 q^{51} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} - 328085114005440 q^{55} + 530930989929024 q^{56} + 367962034636458 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} - 323879741354070 q^{61} - 419080420491096 q^{62} + 937912020807834 q^{63} + 305944925720704 q^{64} - 1276571708976192 q^{65} - 64815073701480 q^{66} - 1580755169097926 q^{67} - 1393626893610696 q^{68} + 2477726596740672 q^{69} + 1815049064679696 q^{70} - 210694758737760 q^{72} - 3848309724808278 q^{73} + 875633111941836 q^{74} + 6202400876359965 q^{75} - 4351002030861264 q^{76} - 81504772370688 q^{77} + 1907392409236620 q^{78} - 4627311352091750 q^{79} - 8190389938127328 q^{80} + 10888533382697109 q^{81} + 2390391408733340 q^{82} - 510964995024720 q^{84} - 4475888457985856 q^{85} - 894939801424296 q^{86} + 10006046679515040 q^{87} + 669091386916800 q^{88} - 5711067674201568 q^{89} + 714578036612004 q^{90} - 13099912671504460 q^{91} + 7708247605922304 q^{92} + 16815765183369930 q^{93} - 9487273535547696 q^{94} + 8786531038601952 q^{96} - 29795334413211414 q^{97} - 33011660914531290 q^{98} + 8858401034408640 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.17.c \(\chi_{12}(5, \cdot)\) 12.17.c.a 1 1
12.17.c.b 4
12.17.d \(\chi_{12}(7, \cdot)\) 12.17.d.a 16 1

Decomposition of \(S_{17}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{17}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{17}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)