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Properties

Label 242.10
Level 242
Weight 10
Dimension 5356
Nonzero newspaces 4
Sturm bound 36300
Trace bound 1

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Defining parameters

Level: \( N \) = \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(36300\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(242))\).

Total New Old
Modular forms 16495 5356 11139
Cusp forms 16175 5356 10819
Eisenstein series 320 0 320

Trace form

\( 5356 q + 16 q^{2} - 156 q^{3} + 256 q^{4} + 870 q^{5} + 12704 q^{6} - 39072 q^{7} + 4096 q^{8} - 12307 q^{9} + O(q^{10}) \) \( 5356 q + 16 q^{2} - 156 q^{3} + 256 q^{4} + 870 q^{5} + 12704 q^{6} - 39072 q^{7} + 4096 q^{8} - 12307 q^{9} - 186080 q^{10} - 30700 q^{11} + 338944 q^{12} + 650334 q^{13} - 338112 q^{14} - 2592940 q^{15} + 65536 q^{16} + 3064958 q^{17} - 186832 q^{18} + 2285030 q^{19} + 222720 q^{20} - 7630728 q^{21} + 2586524 q^{23} + 3252224 q^{24} - 3569705 q^{25} - 15521696 q^{26} - 4977870 q^{27} + 12243968 q^{28} + 25973050 q^{29} + 1859520 q^{30} + 7447772 q^{31} - 9437184 q^{32} - 30127405 q^{33} - 5028192 q^{34} + 65819940 q^{35} + 18944768 q^{36} + 68745638 q^{37} + 24744320 q^{38} - 32551624 q^{39} - 62054400 q^{40} - 185084138 q^{41} + 73389632 q^{42} + 413095704 q^{43} + 22583040 q^{44} - 586252390 q^{45} - 178980096 q^{46} + 42739108 q^{47} - 10223616 q^{48} + 655970917 q^{49} + 201582960 q^{50} - 307789658 q^{51} - 46936576 q^{52} + 53983934 q^{53} - 642729600 q^{54} - 440231950 q^{55} - 3899392 q^{56} - 72828570 q^{57} + 625041120 q^{58} + 1693208510 q^{59} + 474531840 q^{60} + 430854342 q^{61} + 508100672 q^{62} - 628647176 q^{63} + 16777216 q^{64} - 3880273340 q^{65} - 1121705920 q^{66} - 558018212 q^{67} + 784629248 q^{68} + 4434544416 q^{69} + 771348480 q^{70} + 3703175192 q^{71} + 616583168 q^{72} + 1400919854 q^{73} - 533445152 q^{74} - 6210398810 q^{75} - 586506240 q^{76} - 2907503690 q^{77} - 2001198464 q^{78} + 1151808080 q^{79} + 429260800 q^{80} + 9542274051 q^{81} + 4675368512 q^{82} + 3127749194 q^{83} + 1275123712 q^{84} - 6141215660 q^{85} - 6039553376 q^{86} - 11049949400 q^{87} - 779591680 q^{88} - 2020004410 q^{89} + 2311090080 q^{90} + 9899243492 q^{91} + 4403257344 q^{92} + 24376707068 q^{93} + 3374117248 q^{94} - 11429521720 q^{95} - 163577856 q^{96} - 15075266152 q^{97} - 8932470288 q^{98} - 7065764770 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(242))\)

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
242.10.a \(\chi_{242}(1, \cdot)\) 242.10.a.a 1 1
242.10.a.b 1
242.10.a.c 1
242.10.a.d 1
242.10.a.e 2
242.10.a.f 2
242.10.a.g 3
242.10.a.h 3
242.10.a.i 4
242.10.a.j 4
242.10.a.k 4
242.10.a.l 4
242.10.a.m 8
242.10.a.n 8
242.10.a.o 8
242.10.a.p 8
242.10.a.q 10
242.10.a.r 10
242.10.c \(\chi_{242}(3, \cdot)\) n/a 324 4
242.10.e \(\chi_{242}(23, \cdot)\) n/a 990 10
242.10.g \(\chi_{242}(5, \cdot)\) n/a 3960 40

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)