Properties

Label 6045.2.a
Level 6045
Weight 2
Character orbit a
Rep. character \(\chi_{6045}(1,\cdot)\)
Character field \(\Q\)
Dimension 241
Newforms 35
Sturm bound 1792
Trace bound 11

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Defining parameters

Level: \( N \) = \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6045.a (trivial)
Character field: \(\Q\)
Newforms: \( 35 \)
Sturm bound: \(1792\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6045))\).

Total New Old
Modular forms 904 241 663
Cusp forms 889 241 648
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.

\(3\)\(5\)\(13\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(13\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(19\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(12\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(15\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(17\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(16\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(16\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(14\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(18\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(12\)
Plus space\(+\)\(109\)
Minus space\(-\)\(132\)

Trace form

\(241q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 231q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 241q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(241q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 231q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 241q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 20q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut q^{15} \) \(\mathstrut +\mathstrut 223q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 241q^{25} \) \(\mathstrut +\mathstrut 3q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 50q^{29} \) \(\mathstrut +\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut q^{31} \) \(\mathstrut -\mathstrut 49q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 22q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 231q^{36} \) \(\mathstrut -\mathstrut 74q^{37} \) \(\mathstrut +\mathstrut 60q^{38} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 26q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut q^{45} \) \(\mathstrut +\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 31q^{48} \) \(\mathstrut +\mathstrut 225q^{49} \) \(\mathstrut -\mathstrut 13q^{50} \) \(\mathstrut +\mathstrut 10q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut +\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 72q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 26q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 7q^{60} \) \(\mathstrut +\mathstrut 38q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 207q^{64} \) \(\mathstrut +\mathstrut q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut +\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 72q^{71} \) \(\mathstrut -\mathstrut 33q^{72} \) \(\mathstrut +\mathstrut 42q^{73} \) \(\mathstrut +\mathstrut 50q^{74} \) \(\mathstrut +\mathstrut q^{75} \) \(\mathstrut +\mathstrut 28q^{76} \) \(\mathstrut -\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 5q^{78} \) \(\mathstrut -\mathstrut 72q^{79} \) \(\mathstrut +\mathstrut 31q^{80} \) \(\mathstrut +\mathstrut 241q^{81} \) \(\mathstrut +\mathstrut 78q^{82} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 18q^{85} \) \(\mathstrut -\mathstrut 44q^{86} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 28q^{88} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 3q^{90} \) \(\mathstrut -\mathstrut 104q^{92} \) \(\mathstrut -\mathstrut 7q^{93} \) \(\mathstrut +\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 63q^{96} \) \(\mathstrut -\mathstrut 62q^{97} \) \(\mathstrut -\mathstrut 21q^{98} \) \(\mathstrut -\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6045))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 13 31
6045.2.a.a \(1\) \(48.270\) \(\Q\) None \(-2\) \(-1\) \(-1\) \(-5\) \(+\) \(+\) \(+\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-5q^{7}+\cdots\)
6045.2.a.b \(1\) \(48.270\) \(\Q\) None \(-2\) \(-1\) \(1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.c \(1\) \(48.270\) \(\Q\) None \(-2\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-3q^{7}+\cdots\)
6045.2.a.d \(1\) \(48.270\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
6045.2.a.e \(1\) \(48.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-5\) \(-\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{4}-q^{5}-5q^{7}+q^{9}+q^{11}+\cdots\)
6045.2.a.f \(1\) \(48.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
6045.2.a.g \(1\) \(48.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
6045.2.a.h \(1\) \(48.270\) \(\Q\) None \(1\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
6045.2.a.i \(1\) \(48.270\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
6045.2.a.j \(1\) \(48.270\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
6045.2.a.k \(1\) \(48.270\) \(\Q\) None \(2\) \(1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.l \(1\) \(48.270\) \(\Q\) None \(2\) \(1\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.m \(2\) \(48.270\) \(\Q(\sqrt{17}) \) None \(-4\) \(2\) \(-2\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots\)
6045.2.a.n \(2\) \(48.270\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}-q^{5}+(-1+2\beta )q^{7}+\cdots\)
6045.2.a.o \(2\) \(48.270\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}+2q^{7}+\cdots\)
6045.2.a.p \(2\) \(48.270\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}+(1+\beta )q^{7}+\cdots\)
6045.2.a.q \(3\) \(48.270\) 3.3.148.1 None \(0\) \(3\) \(-3\) \(7\) \(-\) \(+\) \(-\) \(-\) \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
6045.2.a.r \(3\) \(48.270\) 3.3.316.1 None \(1\) \(3\) \(3\) \(8\) \(-\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.s \(5\) \(48.270\) 5.5.230224.1 None \(0\) \(5\) \(5\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{2}+q^{3}+(1+\beta _{4})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
6045.2.a.t \(9\) \(48.270\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-6\) \(9\) \(9\) \(-12\) \(-\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6045.2.a.u \(9\) \(48.270\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(9\) \(9\) \(-5\) \(-\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
6045.2.a.v \(10\) \(48.270\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(10\) \(-10\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.w \(11\) \(48.270\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(-11\) \(-11\) \(4\) \(+\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.x \(12\) \(48.270\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(12\) \(-12\) \(3\) \(-\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.y \(12\) \(48.270\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(12\) \(-12\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.z \(12\) \(48.270\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(-12\) \(-7\) \(+\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.ba \(13\) \(48.270\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(-13\) \(13\) \(-11\) \(+\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bb \(13\) \(48.270\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(13\) \(13\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bc \(14\) \(48.270\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-14\) \(-14\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bd \(14\) \(48.270\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-14\) \(14\) \(5\) \(+\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.be \(15\) \(48.270\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(-15\) \(15\) \(-16\) \(+\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bf \(15\) \(48.270\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(15\) \(-15\) \(-5\) \(-\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.bg \(16\) \(48.270\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(-16\) \(-16\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bh \(17\) \(48.270\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(2\) \(-17\) \(17\) \(18\) \(+\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.bi \(18\) \(48.270\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(4\) \(18\) \(18\) \(8\) \(-\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6045))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6045)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(403))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1209))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2015))\)\(^{\oplus 2}\)