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Properties

Label 14.13
Level 14
Weight 13
Dimension 24
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 156
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(156\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(14))\).

Total New Old
Modular forms 78 24 54
Cusp forms 66 24 42
Eisenstein series 12 0 12

Trace form

\( 24 q + 18144 q^{5} - 274560 q^{7} + 883344 q^{9} + O(q^{10}) \) \( 24 q + 18144 q^{5} - 274560 q^{7} + 883344 q^{9} - 2290176 q^{10} + 1858248 q^{11} - 19920384 q^{14} + 38718576 q^{15} - 101561040 q^{17} + 27955200 q^{18} + 174931848 q^{19} - 328181352 q^{21} - 158561280 q^{22} + 182362320 q^{23} + 242221056 q^{24} + 712442808 q^{25} - 1434682368 q^{26} + 750551040 q^{28} + 841214592 q^{29} - 4355484672 q^{30} + 4583818344 q^{31} + 6054957720 q^{33} - 5377275288 q^{35} - 12704563200 q^{36} + 2520923160 q^{37} - 149506560 q^{38} + 24047398536 q^{39} + 4690280448 q^{40} - 24793666560 q^{42} - 45923130000 q^{43} + 3805691904 q^{44} + 57253352184 q^{45} + 16867823616 q^{46} + 18116171640 q^{47} - 29236210968 q^{49} - 72988591104 q^{50} - 104265089208 q^{51} + 8269578240 q^{52} + 219579799320 q^{53} + 105152205312 q^{54} - 13617856512 q^{56} - 391389922320 q^{57} - 64555868160 q^{58} + 201845459088 q^{59} + 162742616064 q^{60} + 336780254328 q^{61} - 791801608800 q^{63} + 206158430208 q^{64} - 266567464296 q^{65} + 268884080640 q^{66} + 476978379360 q^{67} + 207997009920 q^{68} - 144014169600 q^{70} - 576200885040 q^{71} + 57252249600 q^{72} - 738414283320 q^{73} + 455419915776 q^{74} + 1537028640000 q^{75} - 395118788400 q^{77} - 1037089735680 q^{78} - 380194545360 q^{79} - 76101451776 q^{80} + 527067762984 q^{81} - 302578053120 q^{82} - 41799254016 q^{84} + 463007435472 q^{85} - 451197831168 q^{86} + 1957017683880 q^{87} - 517582356480 q^{88} - 2485007442792 q^{89} + 1947775755600 q^{91} + 216003870720 q^{92} + 1833643690200 q^{93} - 2021298693120 q^{94} - 1240145844336 q^{95} - 496068722688 q^{96} - 647169177600 q^{98} + 2120226098112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.13.b \(\chi_{14}(13, \cdot)\) 14.13.b.a 8 1
14.13.d \(\chi_{14}(3, \cdot)\) 14.13.d.a 16 2

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)