Properties

Label 1530.2.a
Level $1530$
Weight $2$
Character orbit 1530.a
Rep. character $\chi_{1530}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $20$
Sturm bound $648$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1530.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(648\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1530))\).

Total New Old
Modular forms 340 24 316
Cusp forms 309 24 285
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.

\(2\)\(3\)\(5\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(9\)
Minus space\(-\)\(15\)

Trace form

\( 24q + 24q^{4} - 2q^{5} + O(q^{10}) \) \( 24q + 24q^{4} - 2q^{5} + 2q^{10} + 4q^{11} + 24q^{16} - 4q^{17} + 4q^{19} - 2q^{20} + 4q^{22} + 8q^{23} + 24q^{25} + 4q^{26} - 28q^{29} + 8q^{31} + 4q^{35} - 12q^{37} + 16q^{38} + 2q^{40} + 16q^{41} - 8q^{43} + 4q^{44} + 24q^{46} + 32q^{49} + 16q^{53} - 4q^{58} - 12q^{59} + 36q^{61} + 24q^{64} + 4q^{65} + 8q^{67} - 4q^{68} + 12q^{70} + 16q^{71} + 32q^{73} + 12q^{74} + 4q^{76} - 40q^{79} - 2q^{80} - 8q^{82} + 16q^{83} + 2q^{85} + 32q^{86} + 4q^{88} + 4q^{89} + 40q^{91} + 8q^{92} + 12q^{94} - 24q^{97} + 8q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1530))\) 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 17
1530.2.a.a \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.b \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
1530.2.a.c \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.d \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.e \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.f \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots\)
1530.2.a.g \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.h \(1\) \(12.217\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.i \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.j \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.k \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.l \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.m \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.n \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.o \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.p \(1\) \(12.217\) \(\Q\) None \(1\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.q \(2\) \(12.217\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\)
1530.2.a.r \(2\) \(12.217\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+2\beta q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.s \(2\) \(12.217\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.t \(2\) \(12.217\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1530))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1530)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(765))\)\(^{\oplus 2}\)