Properties

Label 2070.2.a
Level $2070$
Weight $2$
Character orbit 2070.a
Rep. character $\chi_{2070}(1,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $26$
Sturm bound $864$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2070))\).

Total New Old
Modular forms 448 34 414
Cusp forms 417 34 383
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.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(12\)
Minus space\(-\)\(22\)

Trace form

\( 34q - 2q^{2} + 34q^{4} - 2q^{8} + O(q^{10}) \) \( 34q - 2q^{2} + 34q^{4} - 2q^{8} - 12q^{11} + 4q^{13} + 8q^{14} + 34q^{16} + 4q^{17} + 12q^{19} + 20q^{22} + 34q^{25} + 4q^{29} - 12q^{31} - 2q^{32} + 12q^{34} - 32q^{37} + 4q^{38} + 8q^{41} - 12q^{43} - 12q^{44} + 24q^{47} + 46q^{49} - 2q^{50} + 4q^{52} + 32q^{53} + 8q^{56} + 4q^{58} + 24q^{59} + 24q^{61} + 34q^{64} - 8q^{65} + 44q^{67} + 4q^{68} + 4q^{70} - 20q^{71} + 28q^{73} + 32q^{74} + 12q^{76} + 56q^{77} + 24q^{79} + 20q^{82} + 20q^{83} + 32q^{85} - 4q^{86} + 20q^{88} + 20q^{89} + 32q^{91} - 8q^{94} + 8q^{95} - 4q^{97} - 18q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2070))\) 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
2070.2.a.a \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
2070.2.a.b \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
2070.2.a.c \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
2070.2.a.d \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.e \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.f \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.g \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
2070.2.a.h \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+6q^{13}+\cdots\)
2070.2.a.i \(1\) \(16.529\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.j \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.k \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.l \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.m \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-4q^{11}+\cdots\)
2070.2.a.n \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.o \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.p \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.q \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.r \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
2070.2.a.s \(1\) \(16.529\) \(\Q\) None \(1\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.t \(2\) \(16.529\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots\)
2070.2.a.u \(2\) \(16.529\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
2070.2.a.v \(2\) \(16.529\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+(2+\beta )q^{7}-q^{8}+\cdots\)
2070.2.a.w \(2\) \(16.529\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(-2\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
2070.2.a.x \(2\) \(16.529\) \(\Q(\sqrt{21}) \) None \(2\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.y \(2\) \(16.529\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(2+\beta )q^{7}+q^{8}+\cdots\)
2070.2.a.z \(3\) \(16.529\) 3.3.1101.1 None \(-3\) \(0\) \(3\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2070))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2070)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 2}\)