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Properties

Label 42.14
Level 42
Weight 14
Dimension 154
Nonzero newspaces 4
Newform subspaces 15
Sturm bound 1344
Trace bound 4

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Defining parameters

Level: \( N \) = \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 15 \)
Sturm bound: \(1344\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(42))\).

Total New Old
Modular forms 648 154 494
Cusp forms 600 154 446
Eisenstein series 48 0 48

Trace form

\( 154 q - 128 q^{2} - 24576 q^{4} + 78840 q^{5} - 186624 q^{6} + 1326240 q^{7} - 524288 q^{8} + 2144118 q^{9} + O(q^{10}) \) \( 154 q - 128 q^{2} - 24576 q^{4} + 78840 q^{5} - 186624 q^{6} + 1326240 q^{7} - 524288 q^{8} + 2144118 q^{9} + 6422016 q^{10} - 1693008 q^{11} - 8920268 q^{13} - 11285504 q^{14} + 45837900 q^{15} - 33554432 q^{16} - 7046160 q^{17} - 487512960 q^{18} + 713839048 q^{19} - 447725568 q^{20} + 229327842 q^{21} - 846389760 q^{22} - 800332092 q^{23} + 1242562560 q^{24} + 1795902394 q^{25} - 902574592 q^{26} - 846184448 q^{28} - 10509284772 q^{29} - 4769414400 q^{30} + 13830824296 q^{31} - 2147483648 q^{32} - 30739237848 q^{33} - 17278179072 q^{34} - 10594657872 q^{35} + 123929124864 q^{36} + 86704064460 q^{37} - 52961762560 q^{38} - 87205249560 q^{39} + 26304577536 q^{40} - 10518633252 q^{41} + 23461822080 q^{42} + 215132428200 q^{43} - 6934560768 q^{44} - 360259393824 q^{45} + 158907219456 q^{46} + 272941642812 q^{47} - 830545046450 q^{49} - 21193206656 q^{50} + 31045024152 q^{51} - 14576402432 q^{52} + 190038840048 q^{53} + 242622823680 q^{54} - 522778836996 q^{55} - 264844083200 q^{56} + 30774972108 q^{57} + 210948062208 q^{58} + 1688582614824 q^{59} + 10331357184 q^{60} - 1676338748948 q^{61} - 56850972160 q^{62} - 24982703400 q^{63} - 3710851743744 q^{64} + 9777868341972 q^{65} + 321232227840 q^{66} - 5078137825744 q^{67} - 28861071360 q^{68} - 3104648386344 q^{69} + 3861940084224 q^{70} + 5266327618440 q^{71} + 1439596806144 q^{72} - 10447943816 q^{73} + 2485898461184 q^{74} - 1721901929256 q^{75} - 5035142709248 q^{76} - 13385743731276 q^{77} - 2807771536128 q^{78} + 3885468306488 q^{79} + 1322715709440 q^{80} + 12057593771214 q^{81} - 7835275911936 q^{82} - 23871146824560 q^{83} - 1849598976000 q^{84} + 37962326258952 q^{85} + 12341489069312 q^{86} - 14220651497256 q^{87} + 3201970470912 q^{88} - 19042831491348 q^{89} - 10095100180992 q^{90} - 34086792004784 q^{91} - 201516417024 q^{92} + 39224403957564 q^{93} + 64250023784448 q^{94} - 1700818197468 q^{95} + 5089536245760 q^{96} - 38094342178328 q^{97} - 4471884796544 q^{98} - 20770960687560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.14.a \(\chi_{42}(1, \cdot)\) 42.14.a.a 1 1
42.14.a.b 1
42.14.a.c 1
42.14.a.d 1
42.14.a.e 2
42.14.a.f 2
42.14.a.g 2
42.14.a.h 2
42.14.a.i 2
42.14.d \(\chi_{42}(41, \cdot)\) 42.14.d.a 36 1
42.14.e \(\chi_{42}(25, \cdot)\) 42.14.e.a 8 2
42.14.e.b 8
42.14.e.c 10
42.14.e.d 10
42.14.f \(\chi_{42}(5, \cdot)\) 42.14.f.a 68 2

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 1}\)