Properties

Label 5070.2.a
Level $5070$
Weight $2$
Character orbit 5070.a
Rep. character $\chi_{5070}(1,\cdot)$
Character field $\Q$
Dimension $102$
Newform subspaces $53$
Sturm bound $2184$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5070.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 53 \)
Sturm bound: \(2184\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5070))\).

Total New Old
Modular forms 1148 102 1046
Cusp forms 1037 102 935
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.

\(2\)\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(40\)
Minus space\(-\)\(62\)

Trace form

\( 102q - 2q^{3} + 102q^{4} - 4q^{7} + 102q^{9} + O(q^{10}) \) \( 102q - 2q^{3} + 102q^{4} - 4q^{7} + 102q^{9} - 2q^{10} - 12q^{11} - 2q^{12} - 12q^{14} + 102q^{16} - 8q^{17} - 4q^{21} - 12q^{22} - 8q^{23} + 102q^{25} - 2q^{27} - 4q^{28} + 8q^{29} - 2q^{30} - 8q^{31} + 12q^{33} + 4q^{34} + 4q^{35} + 102q^{36} + 16q^{37} - 8q^{38} - 2q^{40} + 12q^{41} + 4q^{42} - 8q^{43} - 12q^{44} - 8q^{46} + 16q^{47} - 2q^{48} + 102q^{49} - 8q^{51} + 16q^{53} - 12q^{55} - 12q^{56} - 8q^{57} + 4q^{58} + 20q^{59} - 4q^{61} + 8q^{62} - 4q^{63} + 102q^{64} + 4q^{66} + 8q^{67} - 8q^{68} + 8q^{69} + 4q^{70} - 8q^{71} + 20q^{73} + 28q^{74} - 2q^{75} + 16q^{77} - 8q^{79} + 102q^{81} + 16q^{82} - 4q^{84} + 12q^{85} + 8q^{87} - 12q^{88} + 36q^{89} - 2q^{90} - 8q^{92} - 16q^{93} - 8q^{95} + 28q^{97} + 16q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5070))\) 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 13
5070.2.a.a \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5070.2.a.b \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
5070.2.a.c \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
5070.2.a.d \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.e \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.f \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.g \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5070.2.a.h \(1\) \(40.484\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5070.2.a.i \(1\) \(40.484\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-5\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-5q^{7}+\cdots\)
5070.2.a.j \(1\) \(40.484\) \(\Q\) None \(-1\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.k \(1\) \(40.484\) \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
5070.2.a.l \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
5070.2.a.m \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
5070.2.a.n \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.o \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.p \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.q \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(1\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots\)
5070.2.a.r \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(1\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots\)
5070.2.a.s \(1\) \(40.484\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5070.2.a.t \(1\) \(40.484\) \(\Q\) None \(1\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.u \(1\) \(40.484\) \(\Q\) None \(1\) \(1\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
5070.2.a.v \(1\) \(40.484\) \(\Q\) None \(1\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.w \(1\) \(40.484\) \(\Q\) None \(1\) \(1\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
5070.2.a.x \(1\) \(40.484\) \(\Q\) None \(1\) \(1\) \(1\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+5q^{7}+\cdots\)
5070.2.a.y \(2\) \(40.484\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(-4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.z \(2\) \(40.484\) \(\Q(\sqrt{13}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.ba \(2\) \(40.484\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(-6\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
5070.2.a.bb \(2\) \(40.484\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-2\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.bc \(2\) \(40.484\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots\)
5070.2.a.bd \(2\) \(40.484\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5070.2.a.be \(2\) \(40.484\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(6\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
5070.2.a.bf \(2\) \(40.484\) \(\Q(\sqrt{13}) \) None \(2\) \(-2\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5070.2.a.bg \(2\) \(40.484\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.bh \(2\) \(40.484\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.bi \(2\) \(40.484\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(2\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
5070.2.a.bj \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bk \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bl \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(3\) \(8\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bm \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(3\) \(8\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bn \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(-3\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.bo \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(-3\) \(10\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(3+\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bp \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(3\) \(-6\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
5070.2.a.bq \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(3\) \(6\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.br \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(-3\) \(-8\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots\)
5070.2.a.bs \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(-3\) \(-8\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots\)
5070.2.a.bt \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bu \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bv \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-3\) \(-6\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
5070.2.a.bw \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-3\) \(6\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bx \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(3\) \(-10\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-3+\cdots)q^{7}+\cdots\)
5070.2.a.by \(3\) \(40.484\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(3\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bz \(4\) \(40.484\) 4.4.131472.2 None \(-4\) \(4\) \(4\) \(-2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-\beta _{1}q^{7}+\cdots\)
5070.2.a.ca \(4\) \(40.484\) 4.4.131472.2 None \(4\) \(4\) \(-4\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5070))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5070)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2535))\)\(^{\oplus 2}\)