Properties

Label 2624.2.a
Level $2624$
Weight $2$
Character orbit 2624.a
Rep. character $\chi_{2624}(1,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $28$
Sturm bound $672$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2624.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(672\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2624))\).

Total New Old
Modular forms 348 80 268
Cusp forms 325 80 245
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.

\(2\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(16\)
\(+\)\(-\)\(-\)\(24\)
\(-\)\(+\)\(-\)\(24\)
\(-\)\(-\)\(+\)\(16\)
Plus space\(+\)\(32\)
Minus space\(-\)\(48\)

Trace form

\( 80q + 80q^{9} + O(q^{10}) \) \( 80q + 80q^{9} + 16q^{13} + 16q^{21} + 80q^{25} - 16q^{29} + 48q^{45} + 80q^{49} + 32q^{53} - 16q^{61} + 16q^{69} + 32q^{77} + 80q^{81} + 16q^{85} + 64q^{93} - 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2624))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 41
2624.2.a.a \(1\) \(20.953\) \(\Q\) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(-\) \(q-2q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
2624.2.a.b \(1\) \(20.953\) \(\Q\) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(q-2q^{3}+2q^{5}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2624.2.a.c \(1\) \(20.953\) \(\Q\) None \(0\) \(-2\) \(2\) \(4\) \(-\) \(+\) \(q-2q^{3}+2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
2624.2.a.d \(1\) \(20.953\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(q+2q^{5}-2q^{7}-3q^{9}+4q^{13}-2q^{17}+\cdots\)
2624.2.a.e \(1\) \(20.953\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(q+2q^{5}+2q^{7}-3q^{9}+4q^{13}-2q^{17}+\cdots\)
2624.2.a.f \(1\) \(20.953\) \(\Q\) None \(0\) \(2\) \(-2\) \(2\) \(-\) \(-\) \(q+2q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
2624.2.a.g \(1\) \(20.953\) \(\Q\) None \(0\) \(2\) \(2\) \(-4\) \(+\) \(+\) \(q+2q^{3}+2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
2624.2.a.h \(1\) \(20.953\) \(\Q\) None \(0\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q+2q^{3}+2q^{5}+q^{9}-6q^{11}+4q^{13}+\cdots\)
2624.2.a.i \(2\) \(20.953\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(q+(-1+\beta )q^{3}+(1+\beta )q^{7}+(1-2\beta )q^{9}+\cdots\)
2624.2.a.j \(2\) \(20.953\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(q+\beta q^{3}-2\beta q^{5}+(-2+\beta )q^{7}-q^{9}+\cdots\)
2624.2.a.k \(2\) \(20.953\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{3}+\beta q^{7}-q^{9}-\beta q^{11}+2q^{13}+\cdots\)
2624.2.a.l \(2\) \(20.953\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(q+\beta q^{3}+2\beta q^{5}+(2+\beta )q^{7}-q^{9}+3\beta q^{11}+\cdots\)
2624.2.a.m \(2\) \(20.953\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(-1+\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
2624.2.a.n \(3\) \(20.953\) 3.3.148.1 None \(0\) \(-4\) \(2\) \(2\) \(-\) \(-\) \(q+(-1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
2624.2.a.o \(3\) \(20.953\) 3.3.788.1 None \(0\) \(-2\) \(-2\) \(-4\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2624.2.a.p \(3\) \(20.953\) 3.3.148.1 None \(0\) \(-2\) \(-2\) \(2\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
2624.2.a.q \(3\) \(20.953\) 3.3.148.1 None \(0\) \(0\) \(2\) \(-6\) \(-\) \(-\) \(q+\beta _{2}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
2624.2.a.r \(3\) \(20.953\) 3.3.148.1 None \(0\) \(0\) \(2\) \(6\) \(+\) \(-\) \(q-\beta _{2}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(2-\beta _{2})q^{7}+\cdots\)
2624.2.a.s \(3\) \(20.953\) 3.3.148.1 None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(+\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
2624.2.a.t \(3\) \(20.953\) 3.3.788.1 None \(0\) \(2\) \(-2\) \(4\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2624.2.a.u \(3\) \(20.953\) 3.3.148.1 None \(0\) \(4\) \(2\) \(-2\) \(+\) \(-\) \(q+(1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2624.2.a.v \(4\) \(20.953\) 4.4.25808.1 None \(0\) \(-2\) \(-4\) \(0\) \(+\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2624.2.a.w \(4\) \(20.953\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots\)
2624.2.a.x \(4\) \(20.953\) 4.4.25088.1 None \(0\) \(0\) \(4\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(2\beta _{1}-\beta _{3})q^{7}+\cdots\)
2624.2.a.y \(4\) \(20.953\) 4.4.25808.1 None \(0\) \(2\) \(-4\) \(0\) \(-\) \(+\) \(q+(-\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2624.2.a.z \(7\) \(20.953\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-4\) \(2\) \(6\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{3}-\beta _{5}q^{5}+(1-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
2624.2.a.ba \(7\) \(20.953\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(4\) \(2\) \(-6\) \(+\) \(-\) \(q+(1+\beta _{2})q^{3}-\beta _{5}q^{5}+(-1+\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
2624.2.a.bb \(8\) \(20.953\) 8.8.\(\cdots\).1 None \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(q-\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(656))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1312))\)\(^{\oplus 2}\)