Defining parameters
Level: | \( N \) | \(=\) | \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 468.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(468))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 5 | 91 |
Cusp forms | 73 | 5 | 68 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(-\) | \(-\) | $-$ | \(2\) |
Plus space | \(+\) | \(1\) | ||
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(468))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 13 | |||||||
468.2.a.a | $1$ | $3.737$ | \(\Q\) | None | \(0\) | \(0\) | \(-4\) | \(4\) | $-$ | $+$ | $+$ | \(q-4q^{5}+4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots\) | |
468.2.a.b | $1$ | $3.737$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(-2\) | $-$ | $-$ | $+$ | \(q-2q^{5}-2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots\) | |
468.2.a.c | $1$ | $3.737$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(2\) | $-$ | $-$ | $-$ | \(q+2q^{7}+q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\) | |
468.2.a.d | $1$ | $3.737$ | \(\Q\) | None | \(0\) | \(0\) | \(4\) | \(-2\) | $-$ | $-$ | $-$ | \(q+4q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots\) | |
468.2.a.e | $1$ | $3.737$ | \(\Q\) | None | \(0\) | \(0\) | \(4\) | \(4\) | $-$ | $+$ | $+$ | \(q+4q^{5}+4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(468))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(468)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)