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Properties

Label 14.11
Level 14
Weight 11
Dimension 20
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(14))\).

Total New Old
Modular forms 66 20 46
Cusp forms 54 20 34
Eisenstein series 12 0 12

Trace form

\( 20 q + 486 q^{3} + 1024 q^{4} - 6666 q^{5} + 48952 q^{7} - 291984 q^{9} + O(q^{10}) \) \( 20 q + 486 q^{3} + 1024 q^{4} - 6666 q^{5} + 48952 q^{7} - 291984 q^{9} + 130944 q^{10} + 319590 q^{11} - 248832 q^{12} - 175680 q^{14} - 831276 q^{15} + 524288 q^{16} + 1439502 q^{17} - 3797376 q^{18} - 452814 q^{19} + 2398674 q^{21} + 11305344 q^{22} + 7118562 q^{23} - 9338880 q^{24} - 11813356 q^{25} - 8671872 q^{26} + 13472768 q^{28} + 13725840 q^{29} - 8824512 q^{30} + 87231186 q^{31} - 303597198 q^{33} + 338245698 q^{35} - 79564800 q^{36} + 353266310 q^{37} - 21703872 q^{38} - 907748148 q^{39} - 67043328 q^{40} + 437936256 q^{42} + 1098916184 q^{43} + 163630080 q^{44} - 948611736 q^{45} - 937437120 q^{46} - 985909398 q^{47} + 1310072828 q^{49} + 1710257664 q^{50} + 1418472738 q^{51} - 538871808 q^{52} - 1732281162 q^{53} - 402417216 q^{54} - 313589760 q^{56} + 1316206308 q^{57} + 57753984 q^{58} - 2101762050 q^{59} - 1244058624 q^{60} - 2201391150 q^{61} + 5352628632 q^{63} + 2684354560 q^{64} + 1393126476 q^{65} + 728780544 q^{66} - 3844800518 q^{67} - 737025024 q^{68} - 3342795456 q^{70} - 5617649976 q^{71} - 1944256512 q^{72} + 2008593834 q^{73} + 6012515328 q^{74} + 12301086492 q^{75} - 17051529726 q^{77} - 6534077952 q^{78} - 2946805550 q^{79} + 1747451904 q^{80} + 32268765366 q^{81} + 9636272256 q^{82} - 4671630336 q^{84} - 35250530796 q^{85} - 19348724352 q^{86} + 24592790952 q^{87} + 7264960512 q^{88} + 2541648690 q^{89} - 13403022504 q^{91} + 2334382080 q^{92} - 28584650574 q^{93} + 28852652352 q^{94} + 59354345310 q^{95} + 4781506560 q^{96} - 12356095872 q^{98} - 29545328016 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.11.b \(\chi_{14}(13, \cdot)\) 14.11.b.a 8 1
14.11.d \(\chi_{14}(3, \cdot)\) 14.11.d.a 12 2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)