Properties

Label 2116.2
Level 2116
Weight 2
Dimension 80454
Nonzero newspaces 8
Sturm bound 558624
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2116 = 2^{2} \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(558624\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2116))\).

Total New Old
Modular forms 141526 81862 59664
Cusp forms 137787 80454 57333
Eisenstein series 3739 1408 2331

Trace form

\( 80454 q - 231 q^{2} - 231 q^{4} - 462 q^{5} - 231 q^{6} - 231 q^{8} - 462 q^{9} - 231 q^{10} - 231 q^{12} - 462 q^{13} - 231 q^{14} + 22 q^{15} - 231 q^{16} - 440 q^{17} - 231 q^{18} + 22 q^{19} - 231 q^{20}+ \cdots - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2116))\)

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
2116.2.a \(\chi_{2116}(1, \cdot)\) 2116.2.a.a 1 1
2116.2.a.b 1
2116.2.a.c 1
2116.2.a.d 1
2116.2.a.e 2
2116.2.a.f 2
2116.2.a.g 6
2116.2.a.h 8
2116.2.a.i 10
2116.2.a.j 10
2116.2.b \(\chi_{2116}(2115, \cdot)\) n/a 232 1
2116.2.e \(\chi_{2116}(177, \cdot)\) n/a 420 10
2116.2.h \(\chi_{2116}(63, \cdot)\) n/a 2320 10
2116.2.i \(\chi_{2116}(93, \cdot)\) n/a 1012 22
2116.2.l \(\chi_{2116}(91, \cdot)\) n/a 6028 22
2116.2.m \(\chi_{2116}(9, \cdot)\) n/a 10120 220
2116.2.n \(\chi_{2116}(7, \cdot)\) n/a 60280 220

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2116))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2116)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)