Properties

Label 1503.2.a
Level $1503$
Weight $2$
Character orbit 1503.a
Rep. character $\chi_{1503}(1,\cdot)$
Character field $\Q$
Dimension $69$
Newform subspaces $9$
Sturm bound $336$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1503 = 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1503.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(336\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1503))\).

Total New Old
Modular forms 172 69 103
Cusp forms 165 69 96
Eisenstein series 7 0 7

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

\(3\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(14\)
\(+\)\(-\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(26\)
\(-\)\(-\)\(+\)\(15\)
Plus space\(+\)\(29\)
Minus space\(-\)\(40\)

Trace form

\( 69q + 2q^{2} + 70q^{4} + 4q^{5} - 2q^{7} + 12q^{8} + O(q^{10}) \) \( 69q + 2q^{2} + 70q^{4} + 4q^{5} - 2q^{7} + 12q^{8} + 4q^{10} - 2q^{13} - 6q^{14} + 72q^{16} + 4q^{17} + 4q^{19} + 16q^{20} - 12q^{22} + 6q^{23} + 63q^{25} + 10q^{26} - 8q^{28} + 8q^{29} + 16q^{31} + 26q^{32} + 2q^{34} + 26q^{35} - 8q^{37} + 6q^{40} + 2q^{41} + 4q^{43} + 15q^{44} - 16q^{46} - 28q^{47} + 29q^{49} + 12q^{50} - 2q^{52} - 2q^{53} + 18q^{55} + 2q^{56} - 22q^{58} - 2q^{59} - 4q^{61} + 9q^{62} + 34q^{64} - 18q^{65} + 4q^{67} - 36q^{68} - 32q^{70} - 16q^{71} + 8q^{73} + 4q^{74} + 4q^{76} + 24q^{77} - 30q^{79} + 26q^{80} + 14q^{82} - 18q^{83} + 18q^{85} + 12q^{86} - 40q^{88} + 20q^{89} - 62q^{91} + 44q^{92} + 10q^{94} + 20q^{95} + 2q^{97} - 17q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1503))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 167
1503.2.a.a \(1\) \(12.002\) \(\Q\) None \(-1\) \(0\) \(4\) \(4\) \(-\) \(+\) \(q-q^{2}-q^{4}+4q^{5}+4q^{7}+3q^{8}-4q^{10}+\cdots\)
1503.2.a.b \(2\) \(12.002\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-5\) \(-\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2-\beta )q^{7}+\cdots\)
1503.2.a.c \(5\) \(12.002\) 5.5.38569.1 None \(0\) \(0\) \(1\) \(-4\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots\)
1503.2.a.d \(5\) \(12.002\) 5.5.36497.1 None \(4\) \(0\) \(9\) \(-4\) \(-\) \(+\) \(q+(1-\beta _{3})q^{2}+(1+\beta _{1}-2\beta _{3}+\beta _{4})q^{4}+\cdots\)
1503.2.a.e \(8\) \(12.002\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(0\) \(-7\) \(-4\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{3}+\beta _{5}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1503.2.a.f \(8\) \(12.002\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
1503.2.a.g \(12\) \(12.002\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(-4\) \(11\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{4}+\beta _{6}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1503.2.a.h \(14\) \(12.002\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-6\) \(0\) \(-12\) \(0\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{11}+\cdots)q^{5}+\cdots\)
1503.2.a.i \(14\) \(12.002\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(6\) \(0\) \(12\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1503))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1503)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 2}\)