Properties

Label 6760.2.a
Level $6760$
Weight $2$
Character orbit 6760.a
Rep. character $\chi_{6760}(1,\cdot)$
Character field $\Q$
Dimension $155$
Newform subspaces $42$
Sturm bound $2184$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 6760 = 2^{3} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6760.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 42 \)
Sturm bound: \(2184\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6760))\).

Total New Old
Modular forms 1148 155 993
Cusp forms 1037 155 882
Eisenstein series 111 0 111

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

\(2\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(24\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(21\)
Plus space\(+\)\(72\)
Minus space\(-\)\(83\)

Trace form

\( 155q + 4q^{3} + q^{5} + 4q^{7} + 151q^{9} + O(q^{10}) \) \( 155q + 4q^{3} + q^{5} + 4q^{7} + 151q^{9} - 14q^{17} + 8q^{19} - 8q^{21} - 4q^{23} + 155q^{25} + 16q^{27} - 10q^{29} + 8q^{31} - 16q^{33} + 4q^{35} + 14q^{37} + 6q^{41} + 20q^{43} - 3q^{45} - 4q^{47} + 175q^{49} + 8q^{51} + 2q^{53} - 4q^{55} - 16q^{57} + 16q^{59} + 30q^{61} - 12q^{63} + 8q^{69} - 16q^{71} + 2q^{73} + 4q^{75} + 32q^{77} + 8q^{79} + 99q^{81} - 32q^{83} + 2q^{85} - 72q^{87} + 6q^{89} + 24q^{93} + 4q^{95} + 18q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6760))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 13
6760.2.a.a \(1\) \(53.979\) \(\Q\) None \(0\) \(-3\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(q-3q^{3}-q^{5}+3q^{7}+6q^{9}+5q^{11}+\cdots\)
6760.2.a.b \(1\) \(53.979\) \(\Q\) None \(0\) \(-3\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q-3q^{3}+q^{5}-3q^{7}+6q^{9}-5q^{11}+\cdots\)
6760.2.a.c \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}-3q^{7}-2q^{9}-3q^{11}+\cdots\)
6760.2.a.d \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+q^{15}+\cdots\)
6760.2.a.e \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
6760.2.a.f \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}-3q^{7}-2q^{9}+5q^{11}+\cdots\)
6760.2.a.g \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(1\) \(3\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}+3q^{7}-2q^{9}-q^{11}-q^{15}+\cdots\)
6760.2.a.h \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(1\) \(3\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+3q^{7}-2q^{9}+3q^{11}+\cdots\)
6760.2.a.i \(1\) \(53.979\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q-q^{5}+4q^{7}-3q^{9}-4q^{11}+2q^{17}+\cdots\)
6760.2.a.j \(1\) \(53.979\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{5}-3q^{9}+4q^{11}-6q^{17}-4q^{19}+\cdots\)
6760.2.a.k \(1\) \(53.979\) \(\Q\) None \(0\) \(2\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{3}-q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
6760.2.a.l \(1\) \(53.979\) \(\Q\) None \(0\) \(2\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(q+2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
6760.2.a.m \(1\) \(53.979\) \(\Q\) None \(0\) \(2\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
6760.2.a.n \(2\) \(53.979\) \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(q+(-2+\beta )q^{3}-q^{5}+2q^{7}+(3-4\beta )q^{9}+\cdots\)
6760.2.a.o \(2\) \(53.979\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
6760.2.a.p \(2\) \(53.979\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
6760.2.a.q \(2\) \(53.979\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}+3q^{11}+\cdots\)
6760.2.a.r \(2\) \(53.979\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(2\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-3q^{11}+\cdots\)
6760.2.a.s \(2\) \(53.979\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta q^{3}-q^{5}-2q^{7}+3q^{9}+(2-\beta )q^{11}+\cdots\)
6760.2.a.t \(2\) \(53.979\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots\)
6760.2.a.u \(3\) \(53.979\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
6760.2.a.v \(3\) \(53.979\) 3.3.148.1 None \(0\) \(0\) \(3\) \(2\) \(+\) \(-\) \(-\) \(q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.w \(3\) \(53.979\) 3.3.1016.1 None \(0\) \(1\) \(-3\) \(9\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}-q^{5}+3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6760.2.a.x \(3\) \(53.979\) 3.3.1016.1 None \(0\) \(1\) \(3\) \(-9\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}-3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6760.2.a.y \(3\) \(53.979\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-3\) \(-1\) \(+\) \(+\) \(+\) \(q+(1-\beta _{1}-\beta _{2})q^{3}-q^{5}+\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots\)
6760.2.a.z \(3\) \(53.979\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{3}+q^{5}-\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots\)
6760.2.a.ba \(4\) \(53.979\) 4.4.25488.1 None \(0\) \(0\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bb \(4\) \(53.979\) 4.4.25488.1 None \(0\) \(0\) \(4\) \(-4\) \(+\) \(-\) \(+\) \(q-\beta _{2}q^{3}+q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
6760.2.a.bc \(4\) \(53.979\) 4.4.34868.1 None \(0\) \(2\) \(-4\) \(-6\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
6760.2.a.bd \(4\) \(53.979\) 4.4.34868.1 None \(0\) \(2\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
6760.2.a.be \(6\) \(53.979\) 6.6.406193977.1 None \(0\) \(-2\) \(-6\) \(-1\) \(+\) \(+\) \(+\) \(q-\beta _{3}q^{3}-q^{5}-\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
6760.2.a.bf \(6\) \(53.979\) 6.6.406193977.1 None \(0\) \(-2\) \(6\) \(1\) \(-\) \(-\) \(-\) \(q-\beta _{3}q^{3}+q^{5}+\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
6760.2.a.bg \(6\) \(53.979\) 6.6.7674048.1 None \(0\) \(0\) \(-6\) \(-4\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
6760.2.a.bh \(6\) \(53.979\) 6.6.2249737.1 None \(0\) \(0\) \(-6\) \(2\) \(-\) \(+\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{3}-q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bi \(6\) \(53.979\) 6.6.2249737.1 None \(0\) \(0\) \(6\) \(-2\) \(+\) \(-\) \(-\) \(q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bj \(6\) \(53.979\) 6.6.7674048.1 None \(0\) \(0\) \(6\) \(4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{4}+\beta _{5})q^{7}+\cdots\)
6760.2.a.bk \(8\) \(53.979\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(-8\) \(-6\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.bl \(8\) \(53.979\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(8\) \(6\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.bm \(9\) \(53.979\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(1\) \(-9\) \(7\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{8})q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bn \(9\) \(53.979\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(1\) \(9\) \(-7\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{2}-\beta _{8})q^{7}+\cdots\)
6760.2.a.bo \(12\) \(53.979\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-12\) \(-7\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{10})q^{7}+(2+\cdots)q^{9}+\cdots\)
6760.2.a.bp \(12\) \(53.979\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(12\) \(7\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{10})q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3380))\)\(^{\oplus 2}\)