↑

Properties

Label 3020.2.a
Level $3020$
Weight $2$
Character orbit 3020.a
Rep. character $\chi_{3020}(1,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $9$
Sturm bound $912$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3020 = 2^{2} \cdot 5 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3020.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(912\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3020))\).

Total New Old
Modular forms 462 50 412
Cusp forms 451 50 401
Eisenstein series 11 0 11

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

\(2\)\(5\)\(151\)FrickeDim
\(-\)\(+\)\(+\)$-$\(15\)
\(-\)\(+\)\(-\)$+$\(9\)
\(-\)\(-\)\(+\)$+$\(10\)
\(-\)\(-\)\(-\)$-$\(16\)
Plus space\(+\)\(19\)
Minus space\(-\)\(31\)

Trace form

\( 50 q + 4 q^{3} + 2 q^{5} + 58 q^{9} + O(q^{10}) \) \( 50 q + 4 q^{3} + 2 q^{5} + 58 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{17} + 16 q^{19} + 24 q^{21} + 4 q^{23} + 50 q^{25} + 16 q^{27} + 4 q^{29} - 4 q^{31} + 16 q^{33} + 4 q^{35} - 4 q^{37} + 16 q^{39} + 8 q^{41} + 24 q^{43} + 2 q^{45} + 32 q^{47} + 50 q^{49} + 12 q^{53} - 8 q^{55} - 12 q^{57} - 16 q^{59} - 8 q^{61} + 36 q^{63} + 16 q^{67} - 20 q^{69} + 36 q^{71} + 4 q^{73} + 4 q^{75} - 24 q^{77} - 8 q^{79} + 74 q^{81} - 20 q^{83} + 4 q^{85} - 16 q^{89} + 32 q^{91} - 20 q^{93} - 8 q^{95} - 12 q^{97} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3020))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 151
3020.2.a.a 3020.a 1.a $1$ $24.115$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{9}-3q^{11}+q^{13}+\cdots\)
3020.2.a.b 3020.a 1.a $1$ $24.115$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{9}+4q^{13}-2q^{17}+\cdots\)
3020.2.a.c 3020.a 1.a $1$ $24.115$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}-2q^{9}+2q^{13}+q^{15}+\cdots\)
3020.2.a.d 3020.a 1.a $4$ $24.115$ 4.4.4352.1 None \(0\) \(-4\) \(-4\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}+\beta _{3})q^{3}-q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
3020.2.a.e 3020.a 1.a $4$ $24.115$ 4.4.725.1 None \(0\) \(4\) \(-4\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2}+\beta _{3})q^{3}-q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
3020.2.a.f 3020.a 1.a $6$ $24.115$ 6.6.40310669.1 None \(0\) \(2\) \(6\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}-\beta _{3}q^{7}+(3-\beta _{2}-\beta _{4}+\cdots)q^{9}+\cdots\)
3020.2.a.g 3020.a 1.a $8$ $24.115$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(5\) \(8\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(2-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
3020.2.a.h 3020.a 1.a $10$ $24.115$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-6\) \(10\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{4})q^{7}+\cdots\)
3020.2.a.i 3020.a 1.a $15$ $24.115$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(2\) \(-15\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+\beta _{11}q^{7}+(1-\beta _{1}+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(302))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(755))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1510))\)\(^{\oplus 2}\)