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Properties

Label 2900.2.a
Level $2900$
Weight $2$
Character orbit 2900.a
Rep. character $\chi_{2900}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $13$
Sturm bound $900$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2900.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(900\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2900))\).

Total New Old
Modular forms 468 45 423
Cusp forms 433 45 388
Eisenstein series 35 0 35

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

\(2\)\(5\)\(29\)FrickeDim
\(-\)\(+\)\(+\)$-$\(12\)
\(-\)\(+\)\(-\)$+$\(9\)
\(-\)\(-\)\(+\)$+$\(9\)
\(-\)\(-\)\(-\)$-$\(15\)
Plus space\(+\)\(18\)
Minus space\(-\)\(27\)

Trace form

\( 45 q - 4 q^{3} + 43 q^{9} + O(q^{10}) \) \( 45 q - 4 q^{3} + 43 q^{9} + 4 q^{11} + 4 q^{13} - 6 q^{17} + 10 q^{19} + 4 q^{21} + 12 q^{23} + 2 q^{27} + 3 q^{29} - 18 q^{33} + 6 q^{37} + 2 q^{39} + 2 q^{41} - 16 q^{43} + 8 q^{47} + 45 q^{49} - 28 q^{51} - 16 q^{53} + 36 q^{57} - 48 q^{59} + 10 q^{61} - 16 q^{63} + 8 q^{67} + 4 q^{69} + 40 q^{71} - 6 q^{73} + 4 q^{77} - 12 q^{79} + 49 q^{81} - 16 q^{83} + 30 q^{89} + 36 q^{91} + 18 q^{93} + 18 q^{97} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2900))\) 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 29
2900.2.a.a 2900.a 1.a $1$ $23.157$ \(\Q\) None \(0\) \(-2\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2900.2.a.b 2900.a 1.a $1$ $23.157$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}-2q^{9}+3q^{11}-5q^{13}+\cdots\)
2900.2.a.c 2900.a 1.a $1$ $23.157$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}-2q^{11}+2q^{13}-2q^{19}+8q^{23}+\cdots\)
2900.2.a.d 2900.a 1.a $1$ $23.157$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-4q^{11}+6q^{13}+4q^{17}+\cdots\)
2900.2.a.e 2900.a 1.a $1$ $23.157$ \(\Q\) None \(0\) \(3\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{7}+6q^{9}-q^{11}+3q^{13}+\cdots\)
2900.2.a.f 2900.a 1.a $3$ $23.157$ 3.3.148.1 None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2900.2.a.g 2900.a 1.a $3$ $23.157$ 3.3.564.1 None \(0\) \(-2\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{2})q^{7}+(4+\beta _{1}+\cdots)q^{9}+\cdots\)
2900.2.a.h 2900.a 1.a $4$ $23.157$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+\beta _{2}q^{7}-q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
2900.2.a.i 2900.a 1.a $5$ $23.157$ 5.5.2370465.1 None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
2900.2.a.j 2900.a 1.a $5$ $23.157$ 5.5.3076177.1 None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2900.2.a.k 2900.a 1.a $5$ $23.157$ 5.5.2370465.1 None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
2900.2.a.l 2900.a 1.a $5$ $23.157$ 5.5.3076177.1 None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
2900.2.a.m 2900.a 1.a $10$ $23.157$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{9})q^{7}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(725))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1450))\)\(^{\oplus 2}\)