Properties

Label 1470.2.a
Level $1470$
Weight $2$
Character orbit 1470.a
Rep. character $\chi_{1470}(1,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $22$
Sturm bound $672$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1470))\).

Total New Old
Modular forms 368 26 342
Cusp forms 305 26 279
Eisenstein series 63 0 63

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

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(20\)

Trace form

\( 26q - 2q^{3} + 26q^{4} + 26q^{9} + O(q^{10}) \) \( 26q - 2q^{3} + 26q^{4} + 26q^{9} - 2q^{10} + 4q^{11} - 2q^{12} + 26q^{16} + 8q^{17} - 4q^{22} + 24q^{23} + 26q^{25} + 4q^{26} - 2q^{27} - 8q^{29} + 2q^{30} + 16q^{31} + 4q^{33} - 4q^{34} + 26q^{36} + 56q^{37} + 8q^{38} + 48q^{39} - 2q^{40} + 12q^{41} + 56q^{43} + 4q^{44} + 16q^{47} - 2q^{48} - 8q^{51} - 4q^{55} + 48q^{57} + 4q^{58} + 4q^{59} + 12q^{61} + 8q^{62} + 26q^{64} + 4q^{65} + 12q^{66} + 48q^{67} + 8q^{68} - 8q^{69} - 8q^{71} + 4q^{73} - 20q^{74} - 2q^{75} - 4q^{78} + 40q^{79} + 26q^{81} - 16q^{82} - 32q^{83} - 4q^{85} + 24q^{87} - 4q^{88} - 44q^{89} - 2q^{90} + 24q^{92} + 40q^{93} + 24q^{94} - 24q^{95} - 20q^{97} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\) 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 7
1470.2.a.a \(1\) \(11.738\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
1470.2.a.b \(1\) \(11.738\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
1470.2.a.c \(1\) \(11.738\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
1470.2.a.d \(1\) \(11.738\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1470.2.a.e \(1\) \(11.738\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1470.2.a.f \(1\) \(11.738\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
1470.2.a.g \(1\) \(11.738\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
1470.2.a.h \(1\) \(11.738\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
1470.2.a.i \(1\) \(11.738\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
1470.2.a.j \(1\) \(11.738\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
1470.2.a.k \(1\) \(11.738\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
1470.2.a.l \(1\) \(11.738\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
1470.2.a.m \(1\) \(11.738\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
1470.2.a.n \(1\) \(11.738\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
1470.2.a.o \(1\) \(11.738\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1470.2.a.p \(1\) \(11.738\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1470.2.a.q \(1\) \(11.738\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1470.2.a.r \(1\) \(11.738\) \(\Q\) None \(1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
1470.2.a.s \(2\) \(11.738\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1470.2.a.t \(2\) \(11.738\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
1470.2.a.u \(2\) \(11.738\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
1470.2.a.v \(2\) \(11.738\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1470))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1470)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 2}\)