Defining parameters
Level: | \( N \) | \(=\) | \( 7381 = 11^{2} \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7381.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(1364\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7381))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 694 | 545 | 149 |
Cusp forms | 671 | 545 | 126 |
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.
\(11\) | \(61\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(129\) |
\(+\) | \(-\) | $-$ | \(141\) |
\(-\) | \(+\) | $-$ | \(145\) |
\(-\) | \(-\) | $+$ | \(130\) |
Plus space | \(+\) | \(259\) | |
Minus space | \(-\) | \(286\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7381))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 11 | 61 | |||||||
7381.2.a.a | $1$ | $58.938$ | \(\Q\) | None | \(0\) | \(1\) | \(3\) | \(-2\) | $-$ | $+$ | \(q+q^{3}-2q^{4}+3q^{5}-2q^{7}-2q^{9}+\cdots\) | |
7381.2.a.b | $1$ | $58.938$ | \(\Q\) | None | \(0\) | \(1\) | \(3\) | \(2\) | $-$ | $-$ | \(q+q^{3}-2q^{4}+3q^{5}+2q^{7}-2q^{9}+\cdots\) | |
7381.2.a.c | $1$ | $58.938$ | \(\Q\) | None | \(1\) | \(-2\) | \(-3\) | \(-1\) | $-$ | $-$ | \(q+q^{2}-2q^{3}-q^{4}-3q^{5}-2q^{6}-q^{7}+\cdots\) | |
7381.2.a.d | $2$ | $58.938$ | \(\Q(\sqrt{5}) \) | None | \(-4\) | \(-2\) | \(-3\) | \(-4\) | $+$ | $-$ | \(q-2q^{2}+(-2+2\beta )q^{3}+2q^{4}+(-2+\cdots)q^{5}+\cdots\) | |
7381.2.a.e | $2$ | $58.938$ | \(\Q(\sqrt{5}) \) | None | \(4\) | \(-2\) | \(-3\) | \(4\) | $-$ | $+$ | \(q+2q^{2}+(-2+2\beta )q^{3}+2q^{4}+(-2+\cdots)q^{5}+\cdots\) | |
7381.2.a.f | $3$ | $58.938$ | 3.3.148.1 | None | \(-1\) | \(2\) | \(-1\) | \(3\) | $-$ | $+$ | \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\) | |
7381.2.a.g | $5$ | $58.938$ | 5.5.24217.1 | None | \(2\) | \(0\) | \(-2\) | \(1\) | $-$ | $+$ | \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\) | |
7381.2.a.h | $6$ | $58.938$ | 6.6.2661761.1 | None | \(0\) | \(-1\) | \(-1\) | \(5\) | $-$ | $-$ | \(q-\beta _{3}q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\) | |
7381.2.a.i | $19$ | $58.938$ | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) | None | \(-5\) | \(0\) | \(0\) | \(-9\) | $-$ | $-$ | \(q-\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\) | |
7381.2.a.j | $21$ | $58.938$ | None | \(0\) | \(3\) | \(7\) | \(-5\) | $-$ | $+$ | |||
7381.2.a.k | $24$ | $58.938$ | None | \(-5\) | \(-2\) | \(-4\) | \(-6\) | $-$ | $-$ | |||
7381.2.a.l | $24$ | $58.938$ | None | \(5\) | \(-2\) | \(-4\) | \(6\) | $-$ | $+$ | |||
7381.2.a.m | $25$ | $58.938$ | None | \(-5\) | \(-1\) | \(-1\) | \(-4\) | $+$ | $+$ | |||
7381.2.a.n | $25$ | $58.938$ | None | \(-5\) | \(-1\) | \(-1\) | \(-4\) | $-$ | $-$ | |||
7381.2.a.o | $25$ | $58.938$ | None | \(5\) | \(-1\) | \(-1\) | \(4\) | $-$ | $+$ | |||
7381.2.a.p | $25$ | $58.938$ | None | \(5\) | \(-1\) | \(-1\) | \(4\) | $+$ | $-$ | |||
7381.2.a.q | $50$ | $58.938$ | None | \(-10\) | \(-2\) | \(-2\) | \(-8\) | $+$ | $+$ | |||
7381.2.a.r | $50$ | $58.938$ | None | \(10\) | \(-2\) | \(-2\) | \(8\) | $+$ | $-$ | |||
7381.2.a.s | $54$ | $58.938$ | None | \(-1\) | \(-15\) | \(-14\) | \(-2\) | $-$ | $-$ | |||
7381.2.a.t | $54$ | $58.938$ | None | \(1\) | \(-15\) | \(-14\) | \(2\) | $+$ | $+$ | |||
7381.2.a.u | $64$ | $58.938$ | None | \(-5\) | \(19\) | \(21\) | \(-6\) | $-$ | $+$ | |||
7381.2.a.v | $64$ | $58.938$ | None | \(5\) | \(19\) | \(21\) | \(6\) | $+$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7381))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7381)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(671))\)\(^{\oplus 2}\)