Properties

Label 12.7
Level 12
Weight 7
Dimension 8
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 56
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(12))\).

Total New Old
Modular forms 29 8 21
Cusp forms 19 8 11
Eisenstein series 10 0 10

Trace form

\( 8 q - 10 q^{2} - 6 q^{3} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 484 q^{7} + 1136 q^{8} - 2880 q^{9} + O(q^{10}) \) \( 8 q - 10 q^{2} - 6 q^{3} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 484 q^{7} + 1136 q^{8} - 2880 q^{9} + 84 q^{10} - 972 q^{12} + 1888 q^{13} + 4776 q^{14} - 8640 q^{15} - 9744 q^{16} + 12220 q^{17} + 2430 q^{18} + 11572 q^{19} + 17608 q^{20} - 11172 q^{21} - 13512 q^{22} - 7776 q^{24} + 35828 q^{25} - 59252 q^{26} + 12906 q^{27} - 17808 q^{28} - 84860 q^{29} + 57348 q^{30} - 40892 q^{31} + 61280 q^{32} + 99576 q^{33} + 109404 q^{34} - 37908 q^{36} - 72752 q^{37} - 128088 q^{38} - 15708 q^{39} - 195552 q^{40} - 65252 q^{41} + 210600 q^{42} + 137236 q^{43} + 445008 q^{44} + 62532 q^{45} + 81120 q^{46} - 276048 q^{48} - 229716 q^{49} - 743118 q^{50} - 380160 q^{51} - 179592 q^{52} + 470308 q^{53} + 39366 q^{54} + 570240 q^{55} + 793728 q^{56} - 238836 q^{57} + 529860 q^{58} - 723816 q^{60} + 62512 q^{61} - 513384 q^{62} - 344124 q^{63} - 642432 q^{64} + 321512 q^{65} + 771768 q^{66} - 168716 q^{67} + 690328 q^{68} + 1042848 q^{69} + 938928 q^{70} - 276048 q^{72} - 1511024 q^{73} - 1522916 q^{74} + 61770 q^{75} + 67824 q^{76} - 1487328 q^{77} + 396252 q^{78} - 319484 q^{79} + 1272352 q^{80} + 1313496 q^{81} + 240444 q^{82} - 143856 q^{84} - 1466040 q^{85} - 1154568 q^{86} + 665280 q^{87} + 489600 q^{88} + 730924 q^{89} - 20412 q^{90} + 1267112 q^{91} - 1338816 q^{92} + 39084 q^{93} - 390288 q^{94} + 624672 q^{96} + 5048464 q^{97} + 1604918 q^{98} - 570240 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
12.7.c \(\chi_{12}(5, \cdot)\) 12.7.c.a 2 1
12.7.d \(\chi_{12}(7, \cdot)\) 12.7.d.a 6 1

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)