Properties

Label 14.7
Level 14
Weight 7
Dimension 12
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 84
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(14))\).

Total New Old
Modular forms 42 12 30
Cusp forms 30 12 18
Eisenstein series 12 0 12

Trace form

\( 12 q - 336 q^{5} + 960 q^{7} + 1848 q^{9} + O(q^{10}) \) \( 12 q - 336 q^{5} + 960 q^{7} + 1848 q^{9} - 2016 q^{10} - 5796 q^{11} + 4752 q^{14} + 22824 q^{15} - 17304 q^{17} - 16800 q^{18} - 32004 q^{19} + 29244 q^{21} + 26784 q^{22} + 36456 q^{23} + 10752 q^{24} - 36036 q^{25} - 4704 q^{26} + 2304 q^{28} - 48576 q^{29} - 32592 q^{30} - 3108 q^{31} + 3276 q^{33} + 14028 q^{35} - 13440 q^{36} - 29316 q^{37} + 155568 q^{38} + 309372 q^{39} + 64512 q^{40} - 235296 q^{42} - 342072 q^{43} - 185472 q^{44} - 172116 q^{45} - 160272 q^{46} + 313908 q^{47} - 277836 q^{49} + 403584 q^{50} + 411516 q^{51} + 255360 q^{52} + 527100 q^{53} + 386064 q^{54} - 39936 q^{56} - 554280 q^{57} - 1010016 q^{58} - 835464 q^{59} - 572544 q^{60} - 995316 q^{61} + 1090608 q^{63} + 393216 q^{64} + 1301916 q^{65} + 1673280 q^{66} + 214032 q^{67} + 553728 q^{68} - 470736 q^{70} - 261480 q^{71} - 537600 q^{72} - 1617084 q^{73} - 2139648 q^{74} - 2042208 q^{75} + 1146600 q^{77} + 2424192 q^{78} + 2163000 q^{79} + 344064 q^{80} + 925092 q^{81} + 66528 q^{82} - 509952 q^{84} + 73224 q^{85} - 2907744 q^{86} - 2057076 q^{87} - 354816 q^{88} + 739116 q^{89} + 1124280 q^{91} + 1562880 q^{92} + 971964 q^{93} + 3795120 q^{94} + 535080 q^{95} - 344064 q^{96} - 2704416 q^{98} - 5957856 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(14))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
14.7.b \(\chi_{14}(13, \cdot)\) 14.7.b.a 4 1
14.7.d \(\chi_{14}(3, \cdot)\) 14.7.d.a 8 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

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