Properties

Label 2496.2.a
Level $2496$
Weight $2$
Character orbit 2496.a
Rep. character $\chi_{2496}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $38$
Sturm bound $896$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(896\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2496))\).

Total New Old
Modular forms 472 48 424
Cusp forms 425 48 377
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(20\)
Minus space\(-\)\(28\)

Trace form

\( 48q + 48q^{9} + O(q^{10}) \) \( 48q + 48q^{9} + 48q^{25} + 32q^{29} + 32q^{37} + 48q^{49} + 32q^{53} + 32q^{61} + 32q^{69} - 64q^{77} + 48q^{81} - 64q^{85} + 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2496))\) 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
2496.2.a.a \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-4q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
2496.2.a.b \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.c \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{5}+q^{9}-q^{13}+2q^{15}+\cdots\)
2496.2.a.d \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.e \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
2496.2.a.f \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
2496.2.a.g \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{9}-6q^{11}+q^{13}+2q^{17}+\cdots\)
2496.2.a.h \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}-q^{13}-6q^{17}+\cdots\)
2496.2.a.i \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}-q^{13}+2q^{17}+\cdots\)
2496.2.a.j \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q-q^{3}+4q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
2496.2.a.k \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(2\) \(-4\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
2496.2.a.l \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{5}+q^{9}+4q^{11}-q^{13}+\cdots\)
2496.2.a.m \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(2\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
2496.2.a.n \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(4\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.o \(1\) \(19.931\) \(\Q\) None \(0\) \(-1\) \(4\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+4q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.p \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}-4q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
2496.2.a.q \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.r \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
2496.2.a.s \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+q^{9}-q^{13}-2q^{15}+\cdots\)
2496.2.a.t \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(-2\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
2496.2.a.u \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q+q^{3}-4q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
2496.2.a.v \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{7}+q^{9}-q^{13}-6q^{17}+\cdots\)
2496.2.a.w \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{7}+q^{9}-q^{13}+2q^{17}+\cdots\)
2496.2.a.x \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{9}+6q^{11}+q^{13}+2q^{17}+\cdots\)
2496.2.a.y \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
2496.2.a.z \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}+2q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
2496.2.a.ba \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+q^{9}-4q^{11}-q^{13}+\cdots\)
2496.2.a.bb \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+4q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
2496.2.a.bc \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(4\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
2496.2.a.bd \(1\) \(19.931\) \(\Q\) None \(0\) \(1\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
2496.2.a.be \(2\) \(19.931\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1-\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
2496.2.a.bf \(2\) \(19.931\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.bg \(2\) \(19.931\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-6\) \(-\) \(+\) \(-\) \(q-q^{3}+(1+\beta )q^{5}+(-3+\beta )q^{7}+q^{9}+\cdots\)
2496.2.a.bh \(2\) \(19.931\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1-\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
2496.2.a.bi \(2\) \(19.931\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-2q^{11}+\cdots\)
2496.2.a.bj \(2\) \(19.931\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(6\) \(-\) \(-\) \(-\) \(q+q^{3}+(1+\beta )q^{5}+(3-\beta )q^{7}+q^{9}+\cdots\)
2496.2.a.bk \(3\) \(19.931\) 3.3.148.1 None \(0\) \(-3\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
2496.2.a.bl \(3\) \(19.931\) 3.3.148.1 None \(0\) \(3\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2496))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2496)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 2}\)