Properties

Label 2646.2.a
Level $2646$
Weight $2$
Character orbit 2646.a
Rep. character $\chi_{2646}(1,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $42$
Sturm bound $1008$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 42 \)
Sturm bound: \(1008\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2646))\).

Total New Old
Modular forms 552 54 498
Cusp forms 457 54 403
Eisenstein series 95 0 95

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(9\)
Plus space\(+\)\(22\)
Minus space\(-\)\(32\)

Trace form

\( 54q + 54q^{4} + O(q^{10}) \) \( 54q + 54q^{4} - 10q^{10} + 54q^{16} + 4q^{19} - 6q^{22} + 40q^{25} + 6q^{31} - 8q^{34} + 16q^{37} - 10q^{40} + 64q^{43} - 4q^{46} + 58q^{55} + 4q^{58} + 54q^{64} + 32q^{67} + 38q^{73} + 4q^{76} + 52q^{79} - 12q^{82} + 8q^{85} - 6q^{88} + 36q^{94} - 46q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2646))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
2646.2.a.a \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-3q^{11}+\cdots\)
2646.2.a.b \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-4q^{13}+\cdots\)
2646.2.a.c \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-5q^{11}+\cdots\)
2646.2.a.d \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+2q^{11}+\cdots\)
2646.2.a.e \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-q^{11}+\cdots\)
2646.2.a.f \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{8}-5q^{13}+q^{16}+3q^{17}+\cdots\)
2646.2.a.g \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{8}+6q^{11}-5q^{13}+\cdots\)
2646.2.a.h \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{8}+6q^{11}+5q^{13}+\cdots\)
2646.2.a.i \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots\)
2646.2.a.j \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots\)
2646.2.a.k \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-5q^{11}+\cdots\)
2646.2.a.l \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+2q^{11}+\cdots\)
2646.2.a.m \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(3\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+4q^{13}+\cdots\)
2646.2.a.n \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(3\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
2646.2.a.o \(1\) \(21.128\) \(\Q\) None \(-1\) \(0\) \(4\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+4q^{5}-q^{8}-4q^{10}+4q^{11}+\cdots\)
2646.2.a.p \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}-4q^{11}+\cdots\)
2646.2.a.q \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
2646.2.a.r \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+4q^{13}+\cdots\)
2646.2.a.s \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-2q^{11}+\cdots\)
2646.2.a.t \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+5q^{11}+\cdots\)
2646.2.a.u \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots\)
2646.2.a.v \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+5q^{11}+\cdots\)
2646.2.a.w \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{8}-6q^{11}-5q^{13}+\cdots\)
2646.2.a.x \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-6q^{11}+5q^{13}+\cdots\)
2646.2.a.y \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{8}-5q^{13}+q^{16}-3q^{17}+\cdots\)
2646.2.a.z \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots\)
2646.2.a.ba \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-2q^{11}+\cdots\)
2646.2.a.bb \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+5q^{11}+\cdots\)
2646.2.a.bc \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-4q^{13}+\cdots\)
2646.2.a.bd \(1\) \(21.128\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+3q^{11}+\cdots\)
2646.2.a.be \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-6\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+(-3+\beta )q^{5}-q^{8}+(3+\cdots)q^{10}+\cdots\)
2646.2.a.bf \(2\) \(21.128\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
2646.2.a.bg \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+(2+\cdots)q^{11}+\cdots\)
2646.2.a.bh \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+(2+\cdots)q^{11}+\cdots\)
2646.2.a.bi \(2\) \(21.128\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.a.bj \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(6\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(3+\beta )q^{5}-q^{8}+(-3+\cdots)q^{10}+\cdots\)
2646.2.a.bk \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-6\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(-3+\beta )q^{5}+q^{8}+(-3+\cdots)q^{10}+\cdots\)
2646.2.a.bl \(2\) \(21.128\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.a.bm \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2646.2.a.bn \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2646.2.a.bo \(2\) \(21.128\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
2646.2.a.bp \(2\) \(21.128\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(6\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+(3+\beta )q^{5}+q^{8}+(3+\beta )q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2646))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2646)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1323))\)\(^{\oplus 2}\)