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

\( 18475 q - 48 q^{2} + 764 q^{3} - 802 q^{4} + 3424 q^{5} - 32822 q^{6} + 2700 q^{7} + 191142 q^{8} - 195359 q^{9} - 170805 q^{10} + 384006 q^{11} + 552550 q^{12} - 1464884 q^{13} + 50580 q^{14} - 73915 q^{15}+ \cdots - 4435245064 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

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