Properties

Label 2736.2.a
Level $2736$
Weight $2$
Character orbit 2736.a
Rep. character $\chi_{2736}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $32$
Sturm bound $960$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 32 \)
Sturm bound: \(960\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2736))\).

Total New Old
Modular forms 504 45 459
Cusp forms 457 45 412
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.

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(18\)
Minus space\(-\)\(27\)

Trace form

\( 45q - 2q^{5} - 2q^{7} + O(q^{10}) \) \( 45q - 2q^{5} - 2q^{7} - 10q^{11} - 2q^{13} + 2q^{17} + 3q^{19} + 8q^{23} + 55q^{25} + 14q^{29} - 6q^{35} + 6q^{37} + 2q^{41} + 18q^{43} + 10q^{47} + 53q^{49} + 6q^{53} + 14q^{55} + 8q^{59} - 2q^{61} + 12q^{65} - 4q^{67} - 44q^{71} + 18q^{73} + 24q^{77} + 8q^{79} + 8q^{83} - 4q^{85} + 2q^{89} + 8q^{91} + 8q^{95} - 6q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19
2736.2.a.a \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-4\) \(-4\) \(+\) \(-\) \(+\) \(q-4q^{5}-4q^{7}-4q^{11}-4q^{13}-6q^{17}+\cdots\)
2736.2.a.b \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{5}-6q^{11}+2q^{13}-4q^{17}+q^{19}+\cdots\)
2736.2.a.c \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(q-3q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.d \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}-4q^{11}+2q^{13}+6q^{17}+q^{19}+\cdots\)
2736.2.a.e \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{5}+2q^{13}-2q^{17}+q^{19}-q^{25}+\cdots\)
2736.2.a.f \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{5}+2q^{11}-4q^{13}+q^{19}+8q^{23}+\cdots\)
2736.2.a.g \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}+2q^{11}+2q^{13}-6q^{17}+q^{19}+\cdots\)
2736.2.a.h \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(-\) \(-\) \(-\) \(q-q^{5}-3q^{7}-3q^{11}-6q^{13}-3q^{17}+\cdots\)
2736.2.a.i \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(q-q^{5}+3q^{7}-5q^{11}-2q^{13}+q^{17}+\cdots\)
2736.2.a.j \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q-4q^{7}+4q^{11}+2q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.k \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(q-3q^{7}+2q^{11}+q^{13}+5q^{17}-q^{19}+\cdots\)
2736.2.a.l \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{11}-2q^{13}+4q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.m \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{11}-2q^{13}-4q^{17}-q^{19}+2q^{23}+\cdots\)
2736.2.a.n \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+q^{7}-6q^{11}+5q^{13}-3q^{17}-q^{19}+\cdots\)
2736.2.a.o \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(+\) \(q+4q^{7}-4q^{13}-6q^{17}-q^{19}-6q^{23}+\cdots\)
2736.2.a.p \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(+\) \(-\) \(-\) \(q+q^{5}+3q^{7}-3q^{11}-4q^{13}-5q^{17}+\cdots\)
2736.2.a.q \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(-\) \(-\) \(-\) \(q+q^{5}+3q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.r \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{5}-2q^{11}-4q^{13}+q^{19}-8q^{23}+\cdots\)
2736.2.a.s \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{5}+6q^{13}+6q^{17}+q^{19}+4q^{23}+\cdots\)
2736.2.a.t \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(-\) \(+\) \(q+3q^{5}-q^{7}-5q^{11}-6q^{13}+5q^{17}+\cdots\)
2736.2.a.u \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(3\) \(3\) \(+\) \(-\) \(+\) \(q+3q^{5}+3q^{7}-q^{11}-2q^{13}+5q^{17}+\cdots\)
2736.2.a.v \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(3\) \(5\) \(-\) \(-\) \(-\) \(q+3q^{5}+5q^{7}+q^{11}+2q^{13}+q^{17}+\cdots\)
2736.2.a.w \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(4\) \(-3\) \(-\) \(-\) \(-\) \(q+4q^{5}-3q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots\)
2736.2.a.x \(1\) \(21.847\) \(\Q\) None \(0\) \(0\) \(4\) \(0\) \(+\) \(+\) \(-\) \(q+4q^{5}+6q^{11}+2q^{13}+4q^{17}+q^{19}+\cdots\)
2736.2.a.y \(2\) \(21.847\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-1+\cdots)q^{11}+\cdots\)
2736.2.a.z \(2\) \(21.847\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(q-\beta q^{5}-\beta q^{7}+(4-\beta )q^{11}-2\beta q^{13}+\cdots\)
2736.2.a.ba \(2\) \(21.847\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-6\) \(-\) \(+\) \(-\) \(q+\beta q^{5}-3q^{7}-\beta q^{11}+2q^{13}-3\beta q^{17}+\cdots\)
2736.2.a.bb \(2\) \(21.847\) \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(1\) \(3\) \(+\) \(-\) \(+\) \(q+\beta q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots\)
2736.2.a.bc \(3\) \(21.847\) 3.3.892.1 None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2736.2.a.bd \(3\) \(21.847\) 3.3.961.1 None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.a.be \(3\) \(21.847\) 3.3.892.1 None \(0\) \(0\) \(2\) \(2\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{11}+\cdots\)
2736.2.a.bf \(4\) \(21.847\) 4.4.13068.1 None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2736))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2736)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 2}\)