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Properties

Label 245.10
Level 245
Weight 10
Dimension 18475
Nonzero newspaces 12
Sturm bound 47040
Trace bound 2

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Defining parameters

Level: \( N \) = \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(47040\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(245))\).

Total New Old
Modular forms 21408 18765 2643
Cusp forms 20928 18475 2453
Eisenstein series 480 290 190

Trace form

\( 18475 q - 48 q^{2} + 764 q^{3} - 802 q^{4} + 3424 q^{5} - 32822 q^{6} + 2700 q^{7} + 191142 q^{8} - 195359 q^{9} + O(q^{10}) \) \( 18475 q - 48 q^{2} + 764 q^{3} - 802 q^{4} + 3424 q^{5} - 32822 q^{6} + 2700 q^{7} + 191142 q^{8} - 195359 q^{9} - 170805 q^{10} + 384006 q^{11} + 552550 q^{12} - 1464884 q^{13} + 50580 q^{14} - 73915 q^{15} + 4704166 q^{16} + 4417464 q^{17} - 4824784 q^{18} - 4816938 q^{19} - 5967707 q^{20} - 2299476 q^{21} - 2843494 q^{22} + 19628700 q^{23} + 41307894 q^{24} - 9545258 q^{25} - 39868554 q^{26} - 33699166 q^{27} - 10437780 q^{28} + 20712084 q^{29} - 56980187 q^{30} + 50123146 q^{31} + 72517386 q^{32} - 35008934 q^{33} - 101908614 q^{34} + 4597998 q^{35} + 282506102 q^{36} - 17267736 q^{37} + 68875302 q^{38} - 56084242 q^{39} + 110952001 q^{40} - 169963908 q^{41} - 270430482 q^{42} + 130323748 q^{43} - 97735602 q^{44} - 228605882 q^{45} + 174441730 q^{46} + 192027936 q^{47} + 1050020176 q^{48} + 736428096 q^{49} - 226120842 q^{50} - 39476558 q^{51} - 1546775178 q^{52} - 758558304 q^{53} - 1648502954 q^{54} - 480985097 q^{55} + 375492840 q^{56} + 41454626 q^{57} + 3450291034 q^{58} + 1819334214 q^{59} + 2430740305 q^{60} - 1134702780 q^{61} - 2142633066 q^{62} - 700968216 q^{63} - 2696093498 q^{64} - 2038924057 q^{65} - 3820418710 q^{66} - 780530176 q^{67} + 8332726470 q^{68} + 9456940146 q^{69} + 4076127555 q^{70} - 1809362478 q^{71} - 7776868422 q^{72} - 6482219696 q^{73} - 5874112950 q^{74} - 4528667071 q^{75} - 1157649462 q^{76} + 2394310464 q^{77} + 4374611986 q^{78} + 877830466 q^{79} + 9025828912 q^{80} - 7479397739 q^{81} - 5994472112 q^{82} - 2174495208 q^{83} + 16974273132 q^{84} - 4275078339 q^{85} + 8254928772 q^{86} + 5040631010 q^{87} - 15310045332 q^{88} - 2697791544 q^{89} - 13874086072 q^{90} - 6213070806 q^{91} + 5766588816 q^{92} + 575592618 q^{93} + 14110394076 q^{94} - 1418382625 q^{95} + 19919799236 q^{96} - 3676494306 q^{97} + 31157379696 q^{98} - 4435245064 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(245))\)

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
245.10.a \(\chi_{245}(1, \cdot)\) 245.10.a.a 1 1
245.10.a.b 1
245.10.a.c 2
245.10.a.d 2
245.10.a.e 4
245.10.a.f 5
245.10.a.g 6
245.10.a.h 9
245.10.a.i 9
245.10.a.j 11
245.10.a.k 11
245.10.a.l 13
245.10.a.m 13
245.10.a.n 18
245.10.a.o 18
245.10.b \(\chi_{245}(99, \cdot)\) n/a 180 1
245.10.e \(\chi_{245}(116, \cdot)\) n/a 240 2
245.10.f \(\chi_{245}(48, \cdot)\) n/a 352 2
245.10.j \(\chi_{245}(79, \cdot)\) n/a 352 2
245.10.k \(\chi_{245}(36, \cdot)\) n/a 1008 6
245.10.l \(\chi_{245}(68, \cdot)\) n/a 704 4
245.10.p \(\chi_{245}(29, \cdot)\) n/a 1500 6
245.10.q \(\chi_{245}(11, \cdot)\) n/a 2016 12
245.10.s \(\chi_{245}(13, \cdot)\) n/a 3000 12
245.10.t \(\chi_{245}(4, \cdot)\) n/a 3000 12
245.10.x \(\chi_{245}(3, \cdot)\) n/a 6000 24

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(245)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 1}\)