Properties

Label 6030.2.a
Level 6030
Weight 2
Character orbit a
Rep. character \(\chi_{6030}(1,\cdot)\)
Character field \(\Q\)
Dimension 110
Newforms 51
Sturm bound 2448
Trace bound 13

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Defining parameters

Level: \( N \) = \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6030.a (trivial)
Character field: \(\Q\)
Newforms: \( 51 \)
Sturm bound: \(2448\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6030))\).

Total New Old
Modular forms 1240 110 1130
Cusp forms 1209 110 1099
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.

\(2\)\(3\)\(5\)\(67\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(46\)
Minus space\(-\)\(64\)

Trace form

\(110q \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(110q \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 110q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 28q^{29} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 98q^{49} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 48q^{59} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 110q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 28q^{73} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 24q^{85} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 56q^{89} \) \(\mathstrut +\mathstrut 72q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 12q^{94} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut 16q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6030))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 67
6030.2.a.a \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6030.2.a.b \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots\)
6030.2.a.c \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}+q^{10}+\cdots\)
6030.2.a.d \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(-5\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.e \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.f \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.g \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.h \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.i \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.j \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.k \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.l \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.m \(1\) \(48.150\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.n \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.o \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.p \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.q \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.r \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.s \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.t \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.u \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.v \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.w \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.x \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-4q^{11}+\cdots\)
6030.2.a.y \(1\) \(48.150\) \(\Q\) None \(1\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
6030.2.a.z \(2\) \(48.150\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(-6\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+(-3+\beta )q^{7}-q^{8}+\cdots\)
6030.2.a.ba \(2\) \(48.150\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+(-2+2\beta )q^{7}-q^{8}+\cdots\)
6030.2.a.bb \(2\) \(48.150\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
6030.2.a.bc \(2\) \(48.150\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+(2+\beta )q^{7}-q^{8}+\cdots\)
6030.2.a.bd \(2\) \(48.150\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+(2+\beta )q^{7}+q^{8}+\cdots\)
6030.2.a.be \(2\) \(48.150\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+(-2+2\beta )q^{7}+q^{8}+\cdots\)
6030.2.a.bf \(2\) \(48.150\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(-1+\beta )q^{7}+q^{8}+\cdots\)
6030.2.a.bg \(2\) \(48.150\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots\)
6030.2.a.bh \(2\) \(48.150\) \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots\)
6030.2.a.bi \(2\) \(48.150\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
6030.2.a.bj \(3\) \(48.150\) 3.3.404.1 None \(-3\) \(0\) \(-3\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+\beta _{1}q^{7}-q^{8}+q^{10}+\cdots\)
6030.2.a.bk \(3\) \(48.150\) 3.3.316.1 None \(-3\) \(0\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+(1-\beta _{1})q^{7}-q^{8}+\cdots\)
6030.2.a.bl \(3\) \(48.150\) 3.3.568.1 None \(-3\) \(0\) \(3\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+(-1-\beta _{2})q^{7}-q^{8}+\cdots\)
6030.2.a.bm \(3\) \(48.150\) 3.3.568.1 None \(-3\) \(0\) \(3\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-\beta _{1}q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.a.bn \(3\) \(48.150\) 3.3.316.1 None \(-3\) \(0\) \(3\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+(\beta _{1}-\beta _{2})q^{7}-q^{8}+\cdots\)
6030.2.a.bo \(3\) \(48.150\) 3.3.756.1 None \(-3\) \(0\) \(3\) \(3\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{1})q^{7}-q^{8}+\cdots\)
6030.2.a.bp \(3\) \(48.150\) 3.3.3132.1 None \(-3\) \(0\) \(3\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+(1+\beta _{1})q^{7}-q^{8}+\cdots\)
6030.2.a.bq \(3\) \(48.150\) 3.3.568.1 None \(3\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+(-1-\beta _{2})q^{7}+q^{8}+\cdots\)
6030.2.a.br \(3\) \(48.150\) 3.3.148.1 None \(3\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+\beta _{1}q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.a.bs \(4\) \(48.150\) 4.4.11324.1 None \(4\) \(0\) \(-4\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
6030.2.a.bt \(4\) \(48.150\) 4.4.15188.1 None \(4\) \(0\) \(4\) \(-5\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
6030.2.a.bu \(4\) \(48.150\) 4.4.70292.1 None \(4\) \(0\) \(4\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+\beta _{1}q^{7}+q^{8}+q^{10}+\cdots\)
6030.2.a.bv \(5\) \(48.150\) 5.5.6517908.1 None \(-5\) \(0\) \(-5\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+\beta _{2}q^{7}-q^{8}+q^{10}+\cdots\)
6030.2.a.bw \(5\) \(48.150\) 5.5.31460256.1 None \(5\) \(0\) \(-5\) \(5\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+(1-\beta _{2})q^{7}+q^{8}+\cdots\)
6030.2.a.bx \(8\) \(48.150\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(-8\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+(1-\beta _{6})q^{7}-q^{8}+\cdots\)
6030.2.a.by \(8\) \(48.150\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(8\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(1-\beta _{6})q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6030))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(402))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(603))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(670))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1206))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2010))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3015))\)\(^{\oplus 2}\)