Properties

Label 5292.2.a
Level $5292$
Weight $2$
Character orbit 5292.a
Rep. character $\chi_{5292}(1,\cdot)$
Character field $\Q$
Dimension $55$
Newform subspaces $28$
Sturm bound $2016$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5292.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(2016\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5292))\).

Total New Old
Modular forms 1080 55 1025
Cusp forms 937 55 882
Eisenstein series 143 0 143

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.
\(-\)\(+\)\(+\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(+\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(26\)
Minus space\(-\)\(29\)

Trace form

\( 55 q + O(q^{10}) \) \( 55 q - 13 q^{13} - 3 q^{19} + 41 q^{25} + 8 q^{31} - 33 q^{37} - 30 q^{43} + 4 q^{55} - 7 q^{61} - 29 q^{67} - 41 q^{73} + 3 q^{79} - 52 q^{85} + 7 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5292))\) 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
5292.2.a.a \(1\) \(42.257\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{5}-2q^{13}-3q^{17}+4q^{19}+6q^{23}+\cdots\)
5292.2.a.b \(1\) \(42.257\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{5}+3q^{11}-2q^{13}+6q^{17}-5q^{19}+\cdots\)
5292.2.a.c \(1\) \(42.257\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{5}+2q^{11}-5q^{17}-2q^{19}+2q^{23}+\cdots\)
5292.2.a.d \(1\) \(42.257\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-7q^{13}+8q^{19}-5q^{25}+11q^{31}+\cdots\)
5292.2.a.e \(1\) \(42.257\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-5q^{13}-8q^{19}-5q^{25}+7q^{31}+\cdots\)
5292.2.a.f \(1\) \(42.257\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{13}+q^{19}-5q^{25}+7q^{31}-10q^{37}+\cdots\)
5292.2.a.g \(1\) \(42.257\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{13}-q^{19}-5q^{25}-7q^{31}-10q^{37}+\cdots\)
5292.2.a.h \(1\) \(42.257\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+5q^{13}+8q^{19}-5q^{25}-7q^{31}+\cdots\)
5292.2.a.i \(1\) \(42.257\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+7q^{13}-8q^{19}-5q^{25}-11q^{31}+\cdots\)
5292.2.a.j \(1\) \(42.257\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+7q^{13}+q^{19}-5q^{25}+4q^{31}-q^{37}+\cdots\)
5292.2.a.k \(1\) \(42.257\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{5}-2q^{11}+5q^{17}-2q^{19}-2q^{23}+\cdots\)
5292.2.a.l \(1\) \(42.257\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(-\) \(q+3q^{5}-3q^{11}-2q^{13}-6q^{17}-5q^{19}+\cdots\)
5292.2.a.m \(1\) \(42.257\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{5}-2q^{13}+3q^{17}+4q^{19}-6q^{23}+\cdots\)
5292.2.a.n \(2\) \(42.257\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-q^{5}-\beta q^{11}-\beta q^{13}+3q^{17}-\beta q^{19}+\cdots\)
5292.2.a.o \(2\) \(42.257\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-\beta q^{5}-\beta q^{11}-6q^{13}-2\beta q^{17}+\cdots\)
5292.2.a.p \(2\) \(42.257\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{5}-\beta q^{11}-2q^{13}+q^{19}-3\beta q^{23}+\cdots\)
5292.2.a.q \(2\) \(42.257\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{5}+2\beta q^{11}-\beta q^{17}-7q^{19}+\cdots\)
5292.2.a.r \(2\) \(42.257\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{5}-2\beta q^{11}-\beta q^{17}+7q^{19}+\cdots\)
5292.2.a.s \(2\) \(42.257\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{5}+\beta q^{11}+2q^{13}-q^{19}+3\beta q^{23}+\cdots\)
5292.2.a.t \(2\) \(42.257\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q+q^{5}+\beta q^{11}-\beta q^{13}-3q^{17}-\beta q^{19}+\cdots\)
5292.2.a.u \(3\) \(42.257\) 3.3.321.1 None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{2}q^{5}+(-2+\beta _{1})q^{11}+(-1-\beta _{2})q^{13}+\cdots\)
5292.2.a.v \(3\) \(42.257\) 3.3.321.1 None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{2}q^{5}+(2-\beta _{1})q^{11}+(1+\beta _{2})q^{13}+\cdots\)
5292.2.a.w \(3\) \(42.257\) 3.3.321.1 None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{2}q^{5}+(-2+\beta _{1})q^{11}+(1+\beta _{2})q^{13}+\cdots\)
5292.2.a.x \(3\) \(42.257\) 3.3.321.1 None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{5}+(2-\beta _{1})q^{11}+(-1-\beta _{2})q^{13}+\cdots\)
5292.2.a.y \(4\) \(42.257\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{11}+3\beta _{1}q^{13}+\cdots\)
5292.2.a.z \(4\) \(42.257\) 4.4.7168.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{3}q^{5}+(2\beta _{1}+\beta _{3})q^{11}+(-3\beta _{1}+\cdots)q^{17}+\cdots\)
5292.2.a.ba \(4\) \(42.257\) 4.4.7168.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{3}q^{5}+(-2\beta _{1}-\beta _{3})q^{11}+(-3\beta _{1}+\cdots)q^{17}+\cdots\)
5292.2.a.bb \(4\) \(42.257\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{11}-3\beta _{1}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5292))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5292)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(756))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1323))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1764))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2646))\)\(^{\oplus 2}\)