Properties

Label 12.11
Level 12
Weight 11
Dimension 13
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 88
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(88\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(12))\).

Total New Old
Modular forms 45 13 32
Cusp forms 35 13 22
Eisenstein series 10 0 10

Trace form

\( 13 q + 22 q^{2} - 9 q^{3} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 1446 q^{7} + 20176 q^{8} - 201123 q^{9} + O(q^{10}) \) \( 13 q + 22 q^{2} - 9 q^{3} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 1446 q^{7} + 20176 q^{8} - 201123 q^{9} - 369196 q^{10} + 310068 q^{12} - 96526 q^{13} - 2495544 q^{14} - 544320 q^{15} + 3590128 q^{16} + 2264420 q^{17} - 433026 q^{18} + 3490638 q^{19} + 1194248 q^{20} - 4224762 q^{21} - 2139528 q^{22} - 6858432 q^{24} + 49074393 q^{25} + 29599340 q^{26} - 42988401 q^{27} - 41542224 q^{28} - 46672708 q^{29} + 19963908 q^{30} + 95608662 q^{31} - 83717408 q^{32} - 101984184 q^{33} + 37514588 q^{34} + 12675852 q^{36} + 342578 q^{37} - 218769048 q^{38} - 230735322 q^{39} + 340155488 q^{40} + 276227780 q^{41} - 15919416 q^{42} + 212264574 q^{43} + 532887504 q^{44} - 188703108 q^{45} - 70057824 q^{46} + 27126576 q^{48} + 506736451 q^{49} + 20815602 q^{50} + 237323520 q^{51} - 959132296 q^{52} - 1522721956 q^{53} - 47829690 q^{54} - 747895680 q^{55} - 632703744 q^{56} + 2297509038 q^{57} + 1851304388 q^{58} - 1708229736 q^{60} - 5795028862 q^{61} - 806085192 q^{62} + 1957482774 q^{63} - 877634432 q^{64} + 6725245912 q^{65} + 1244885112 q^{66} - 2159815314 q^{67} + 3081993176 q^{68} + 1860524640 q^{69} + 598086768 q^{70} - 397124208 q^{72} - 304647190 q^{73} - 9824720260 q^{74} - 470003265 q^{75} + 2750616432 q^{76} - 4577505312 q^{77} + 4510566972 q^{78} + 3731176374 q^{79} + 16715013152 q^{80} + 4399629453 q^{81} + 830592764 q^{82} - 10263359664 q^{84} - 1861503560 q^{85} - 15186172488 q^{86} - 13413677760 q^{87} - 12375555840 q^{88} - 13670065996 q^{89} + 7266884868 q^{90} + 20806156668 q^{91} + 12601016256 q^{92} - 2624301306 q^{93} + 38474881584 q^{94} - 27853204320 q^{96} - 12300326758 q^{97} - 31671844202 q^{98} - 29167931520 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.11.c \(\chi_{12}(5, \cdot)\) 12.11.c.a 1 1
12.11.c.b 2
12.11.d \(\chi_{12}(7, \cdot)\) 12.11.d.a 10 1

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)