Properties

Label 3006.2.a
Level $3006$
Weight $2$
Character orbit 3006.a
Rep. character $\chi_{3006}(1,\cdot)$
Character field $\Q$
Dimension $70$
Newform subspaces $23$
Sturm bound $1008$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3006 = 2 \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3006.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(1008\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3006))\).

Total New Old
Modular forms 512 70 442
Cusp forms 497 70 427
Eisenstein series 15 0 15

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

\(2\)\(3\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(12\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(26\)
Minus space\(-\)\(44\)

Trace form

\( 70q + 70q^{4} - 2q^{5} + O(q^{10}) \) \( 70q + 70q^{4} - 2q^{5} + 2q^{10} - 2q^{13} + 4q^{14} + 70q^{16} - 4q^{17} - 2q^{20} + 4q^{22} + 4q^{23} + 70q^{25} - 10q^{26} + 4q^{29} - 12q^{31} - 4q^{34} - 16q^{35} + 10q^{37} + 16q^{38} + 2q^{40} - 12q^{41} + 6q^{43} + 16q^{46} + 40q^{47} + 98q^{49} - 2q^{52} - 2q^{53} - 20q^{55} + 4q^{56} - 6q^{59} + 4q^{61} - 8q^{62} + 70q^{64} + 40q^{65} + 6q^{67} - 4q^{68} + 8q^{70} + 28q^{71} - 12q^{73} + 10q^{74} + 8q^{77} + 48q^{79} - 2q^{80} + 12q^{82} + 10q^{83} - 12q^{85} + 6q^{86} + 4q^{88} + 32q^{91} + 4q^{92} - 12q^{94} - 8q^{95} - 8q^{97} + 16q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3006))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 167
3006.2.a.a \(1\) \(24.003\) \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
3006.2.a.b \(1\) \(24.003\) \(\Q\) None \(-1\) \(0\) \(3\) \(-3\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-3q^{7}-q^{8}-3q^{10}+\cdots\)
3006.2.a.c \(1\) \(24.003\) \(\Q\) None \(1\) \(0\) \(-3\) \(3\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+3q^{7}+q^{8}-3q^{10}+\cdots\)
3006.2.a.d \(1\) \(24.003\) \(\Q\) None \(1\) \(0\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-2q^{10}+\cdots\)
3006.2.a.e \(1\) \(24.003\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-4q^{13}+q^{16}-6q^{17}+\cdots\)
3006.2.a.f \(1\) \(24.003\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
3006.2.a.g \(2\) \(24.003\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(-6\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+(-3-\beta )q^{7}-q^{8}+\cdots\)
3006.2.a.h \(2\) \(24.003\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(4\) \(-6\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(1+2\beta )q^{5}-3q^{7}-q^{8}+\cdots\)
3006.2.a.i \(2\) \(24.003\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{8}+(-2+\cdots)q^{10}+\cdots\)
3006.2.a.j \(2\) \(24.003\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+(-2+\beta )q^{5}+q^{8}+(-2+\cdots)q^{10}+\cdots\)
3006.2.a.k \(2\) \(24.003\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-6\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(-1+\beta )q^{5}-3q^{7}+q^{8}+\cdots\)
3006.2.a.l \(2\) \(24.003\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(-3-\beta )q^{7}+q^{8}+\cdots\)
3006.2.a.m \(2\) \(24.003\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(-1+2\beta )q^{7}+q^{8}+\cdots\)
3006.2.a.n \(2\) \(24.003\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+(2+\beta )q^{5}+2\beta q^{7}+q^{8}+\cdots\)
3006.2.a.o \(3\) \(24.003\) 3.3.148.1 None \(-3\) \(0\) \(3\) \(-5\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(1-\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
3006.2.a.p \(3\) \(24.003\) 3.3.733.1 None \(-3\) \(0\) \(3\) \(3\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
3006.2.a.q \(3\) \(24.003\) 3.3.1300.1 None \(3\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
3006.2.a.r \(3\) \(24.003\) 3.3.469.1 None \(3\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
3006.2.a.s \(4\) \(24.003\) 4.4.2777.1 None \(-4\) \(0\) \(-5\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
3006.2.a.t \(5\) \(24.003\) 5.5.11256624.1 None \(5\) \(0\) \(1\) \(9\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-\beta _{2}q^{5}+(2-\beta _{4})q^{7}+q^{8}+\cdots\)
3006.2.a.u \(7\) \(24.003\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(-5\) \(7\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
3006.2.a.v \(10\) \(24.003\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(0\) \(-4\) \(6\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}+(1-\beta _{4})q^{7}-q^{8}+\cdots\)
3006.2.a.w \(10\) \(24.003\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(0\) \(4\) \(6\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{4})q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1503))\)\(^{\oplus 2}\)