Properties

Label 2760.2.a
Level $2760$
Weight $2$
Character orbit 2760.a
Rep. character $\chi_{2760}(1,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $23$
Sturm bound $1152$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2760.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(1152\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2760))\).

Total New Old
Modular forms 592 44 548
Cusp forms 561 44 517
Eisenstein series 31 0 31

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

\(2\)\(3\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(18\)
Minus space\(-\)\(26\)

Trace form

\( 44q - 4q^{3} - 8q^{7} + 44q^{9} + O(q^{10}) \) \( 44q - 4q^{3} - 8q^{7} + 44q^{9} + 16q^{17} - 8q^{19} - 8q^{21} + 44q^{25} - 4q^{27} + 16q^{29} - 8q^{31} - 8q^{37} - 8q^{39} - 8q^{43} + 52q^{49} - 48q^{53} - 8q^{57} + 16q^{59} - 56q^{61} - 8q^{63} + 8q^{67} + 16q^{71} + 8q^{73} - 4q^{75} + 24q^{79} + 44q^{81} + 48q^{83} + 8q^{85} + 16q^{87} + 48q^{89} + 16q^{91} + 16q^{95} + 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2760))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 23
2760.2.a.a \(1\) \(22.039\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2760.2.a.b \(1\) \(22.039\) \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+3q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
2760.2.a.c \(1\) \(22.039\) \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
2760.2.a.d \(1\) \(22.039\) \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
2760.2.a.e \(1\) \(22.039\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2760.2.a.f \(1\) \(22.039\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
2760.2.a.g \(1\) \(22.039\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
2760.2.a.h \(1\) \(22.039\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-6q^{17}+\cdots\)
2760.2.a.i \(1\) \(22.039\) \(\Q\) None \(0\) \(1\) \(-1\) \(3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+3q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2760.2.a.j \(1\) \(22.039\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-3q^{7}+q^{9}-4q^{11}+q^{15}+\cdots\)
2760.2.a.k \(1\) \(22.039\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+q^{9}+2q^{11}+q^{15}+6q^{17}+\cdots\)
2760.2.a.l \(2\) \(22.039\) \(\Q(\sqrt{11}) \) None \(0\) \(-2\) \(-2\) \(-6\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-3q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
2760.2.a.m \(2\) \(22.039\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots\)
2760.2.a.n \(2\) \(22.039\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(-1+2\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
2760.2.a.o \(2\) \(22.039\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+\beta q^{7}+q^{9}+4q^{11}+(-2+\cdots)q^{13}+\cdots\)
2760.2.a.p \(2\) \(22.039\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
2760.2.a.q \(2\) \(22.039\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
2760.2.a.r \(3\) \(22.039\) 3.3.316.1 None \(0\) \(3\) \(-3\) \(-6\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-2+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2760.2.a.s \(3\) \(22.039\) 3.3.1436.1 None \(0\) \(3\) \(-3\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2760.2.a.t \(3\) \(22.039\) 3.3.229.1 None \(0\) \(3\) \(3\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(1-\beta _{2})q^{13}+\cdots\)
2760.2.a.u \(3\) \(22.039\) 3.3.568.1 None \(0\) \(3\) \(3\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(1-2\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
2760.2.a.v \(4\) \(22.039\) 4.4.54764.1 None \(0\) \(-4\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)
2760.2.a.w \(5\) \(22.039\) 5.5.20087896.1 None \(0\) \(-5\) \(5\) \(-4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 2}\)