Properties

Label 6045.2.a
Level $6045$
Weight $2$
Character orbit 6045.a
Rep. character $\chi_{6045}(1,\cdot)$
Character field $\Q$
Dimension $241$
Newform subspaces $35$
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: \(\Q\)
Newform subspaces: \( 35 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6045))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 13 31
6045.2.a.a 6045.a 1.a $1$ $48.270$ \(\Q\) None \(-2\) \(-1\) \(-1\) \(-5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-5q^{7}+\cdots\)
6045.2.a.b 6045.a 1.a $1$ $48.270$ \(\Q\) None \(-2\) \(-1\) \(1\) \(2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.c 6045.a 1.a $1$ $48.270$ \(\Q\) None \(-2\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-3q^{7}+\cdots\)
6045.2.a.d 6045.a 1.a $1$ $48.270$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
6045.2.a.e 6045.a 1.a $1$ $48.270$ \(\Q\) None \(0\) \(1\) \(-1\) \(-5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-5q^{7}+q^{9}+q^{11}+\cdots\)
6045.2.a.f 6045.a 1.a $1$ $48.270$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
6045.2.a.g 6045.a 1.a $1$ $48.270$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
6045.2.a.h 6045.a 1.a $1$ $48.270$ \(\Q\) None \(1\) \(-1\) \(-1\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
6045.2.a.i 6045.a 1.a $1$ $48.270$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
6045.2.a.j 6045.a 1.a $1$ $48.270$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
6045.2.a.k 6045.a 1.a $1$ $48.270$ \(\Q\) None \(2\) \(1\) \(-1\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.l 6045.a 1.a $1$ $48.270$ \(\Q\) None \(2\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.m 6045.a 1.a $2$ $48.270$ \(\Q(\sqrt{17}) \) None \(-4\) \(2\) \(-2\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots\)
6045.2.a.n 6045.a 1.a $2$ $48.270$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+(-1+2\beta )q^{7}+\cdots\)
6045.2.a.o 6045.a 1.a $2$ $48.270$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}+2q^{7}+\cdots\)
6045.2.a.p 6045.a 1.a $2$ $48.270$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}+(1+\beta )q^{7}+\cdots\)
6045.2.a.q 6045.a 1.a $3$ $48.270$ 3.3.148.1 None \(0\) \(3\) \(-3\) \(7\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
6045.2.a.r 6045.a 1.a $3$ $48.270$ 3.3.316.1 None \(1\) \(3\) \(3\) \(8\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.s 6045.a 1.a $5$ $48.270$ 5.5.230224.1 None \(0\) \(5\) \(5\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(1+\beta _{4})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
6045.2.a.t 6045.a 1.a $9$ $48.270$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-6\) \(9\) \(9\) \(-12\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6045.2.a.u 6045.a 1.a $9$ $48.270$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(9\) \(9\) \(-5\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
6045.2.a.v 6045.a 1.a $10$ $48.270$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(10\) \(-10\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.w 6045.a 1.a $11$ $48.270$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(-11\) \(-11\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.x 6045.a 1.a $12$ $48.270$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(12\) \(-12\) \(3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.y 6045.a 1.a $12$ $48.270$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(12\) \(-12\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.z 6045.a 1.a $12$ $48.270$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(-12\) \(-7\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.ba 6045.a 1.a $13$ $48.270$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(-13\) \(13\) \(-11\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bb 6045.a 1.a $13$ $48.270$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(13\) \(13\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bc 6045.a 1.a $14$ $48.270$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-14\) \(-14\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bd 6045.a 1.a $14$ $48.270$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-14\) \(14\) \(5\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.be 6045.a 1.a $15$ $48.270$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(-15\) \(15\) \(-16\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bf 6045.a 1.a $15$ $48.270$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(15\) \(-15\) \(-5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.bg 6045.a 1.a $16$ $48.270$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(-16\) \(-16\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bh 6045.a 1.a $17$ $48.270$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(2\) \(-17\) \(17\) \(18\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.bi 6045.a 1.a $18$ $48.270$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(4\) \(18\) \(18\) \(8\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

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

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