Defining parameters
Level: | \( N \) | = | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 8015.a (trivial) |
Character field: | \(\Q\) | ||
Newforms: | \( 15 \) | ||
Sturm bound: | \(1840\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8015))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 924 | 455 | 469 |
Cusp forms | 917 | 455 | 462 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(7\) | \(229\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(52\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(63\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(68\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(45\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(67\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(44\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(41\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(75\) |
Plus space | \(+\) | \(182\) | ||
Minus space | \(-\) | \(273\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 5 | 7 | 229 | |||||||
8015.2.a.a | \(1\) | \(64.000\) | \(\Q\) | None | \(-2\) | \(-3\) | \(1\) | \(1\) | \(-\) | \(-\) | \(-\) | \(q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\) | |
8015.2.a.b | \(1\) | \(64.000\) | \(\Q\) | None | \(-1\) | \(-2\) | \(1\) | \(1\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\) | |
8015.2.a.c | \(1\) | \(64.000\) | \(\Q\) | None | \(-1\) | \(1\) | \(1\) | \(1\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\) | |
8015.2.a.d | \(1\) | \(64.000\) | \(\Q\) | None | \(1\) | \(0\) | \(1\) | \(1\) | \(-\) | \(-\) | \(-\) | \(q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\) | |
8015.2.a.e | \(1\) | \(64.000\) | \(\Q\) | None | \(1\) | \(2\) | \(-1\) | \(-1\) | \(+\) | \(+\) | \(-\) | \(q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\) | |
8015.2.a.f | \(1\) | \(64.000\) | \(\Q\) | None | \(2\) | \(1\) | \(1\) | \(1\) | \(-\) | \(-\) | \(+\) | \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\) | |
8015.2.a.g | \(3\) | \(64.000\) | 3.3.148.1 | None | \(1\) | \(-1\) | \(-3\) | \(-3\) | \(+\) | \(+\) | \(+\) | \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\) | |
8015.2.a.h | \(38\) | \(64.000\) | None | \(-6\) | \(-9\) | \(38\) | \(38\) | \(-\) | \(-\) | \(+\) | |||
8015.2.a.i | \(44\) | \(64.000\) | None | \(-2\) | \(0\) | \(44\) | \(-44\) | \(-\) | \(+\) | \(-\) | |||
8015.2.a.j | \(45\) | \(64.000\) | None | \(-6\) | \(0\) | \(-45\) | \(45\) | \(+\) | \(-\) | \(-\) | |||
8015.2.a.k | \(49\) | \(64.000\) | None | \(-3\) | \(-10\) | \(-49\) | \(-49\) | \(+\) | \(+\) | \(+\) | |||
8015.2.a.l | \(62\) | \(64.000\) | None | \(2\) | \(11\) | \(-62\) | \(-62\) | \(+\) | \(+\) | \(-\) | |||
8015.2.a.m | \(67\) | \(64.000\) | None | \(3\) | \(0\) | \(67\) | \(-67\) | \(-\) | \(+\) | \(+\) | |||
8015.2.a.n | \(68\) | \(64.000\) | None | \(9\) | \(0\) | \(-68\) | \(68\) | \(+\) | \(-\) | \(+\) | |||
8015.2.a.o | \(73\) | \(64.000\) | None | \(7\) | \(14\) | \(73\) | \(73\) | \(-\) | \(-\) | \(-\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8015))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(229))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1603))\)\(^{\oplus 2}\)