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Properties

Label 14.8
Level 14
Weight 8
Dimension 12
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(14))\).

Total New Old
Modular forms 48 12 36
Cusp forms 36 12 24
Eisenstein series 12 0 12

Trace form

\( 12 q + 16 q^{2} - 78 q^{3} + 426 q^{5} - 1104 q^{6} - 1680 q^{7} + 1024 q^{8} + 7656 q^{9} + O(q^{10}) \) \( 12 q + 16 q^{2} - 78 q^{3} + 426 q^{5} - 1104 q^{6} - 1680 q^{7} + 1024 q^{8} + 7656 q^{9} - 3984 q^{10} - 9228 q^{11} - 4992 q^{12} + 20346 q^{13} - 18704 q^{14} + 5208 q^{15} + 83256 q^{17} - 25872 q^{18} - 9642 q^{19} - 21120 q^{20} - 187110 q^{21} + 8736 q^{22} + 82848 q^{23} + 101376 q^{24} + 268080 q^{25} - 68464 q^{26} - 482292 q^{27} - 53760 q^{28} + 99468 q^{29} + 489408 q^{30} + 204324 q^{31} + 65536 q^{32} - 1098084 q^{33} - 236352 q^{34} + 156450 q^{35} + 694272 q^{36} + 182568 q^{37} - 699376 q^{38} + 820224 q^{39} - 254976 q^{40} - 458100 q^{41} + 1169616 q^{42} + 2293212 q^{43} - 590592 q^{44} - 2983938 q^{45} - 118080 q^{46} + 1549020 q^{47} - 319488 q^{48} + 837900 q^{49} - 4155056 q^{50} - 6552756 q^{51} - 1009536 q^{52} + 1444596 q^{53} + 4365216 q^{54} + 15553512 q^{55} + 1383424 q^{56} + 898332 q^{57} - 1177152 q^{58} - 10008282 q^{59} - 4137984 q^{60} - 2006454 q^{61} - 3245536 q^{62} - 4245276 q^{63} + 3145728 q^{64} - 4943316 q^{65} + 2043264 q^{66} + 5548776 q^{67} + 5328384 q^{68} + 6655752 q^{69} + 12656784 q^{70} + 7056504 q^{71} - 1655808 q^{72} - 957276 q^{73} - 4063936 q^{74} - 24940746 q^{75} - 8960640 q^{76} - 16124304 q^{77} - 10532352 q^{78} + 23562912 q^{79} + 1744896 q^{80} + 6576996 q^{81} + 19891584 q^{82} - 22146930 q^{83} + 13195392 q^{84} + 12208980 q^{85} + 14237408 q^{86} + 30809124 q^{87} - 4724736 q^{88} - 20862564 q^{89} - 61136592 q^{90} - 36790026 q^{91} - 16009728 q^{92} + 2129100 q^{93} + 29230944 q^{94} + 42512352 q^{95} + 6488064 q^{96} + 25969044 q^{97} + 26719504 q^{98} + 32055492 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)

We only show spaces with even 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
14.8.a \(\chi_{14}(1, \cdot)\) 14.8.a.a 1 1
14.8.a.b 1
14.8.a.c 2
14.8.c \(\chi_{14}(9, \cdot)\) 14.8.c.a 4 2
14.8.c.b 4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 1}\)