Properties

Label 2900.2.c
Level $2900$
Weight $2$
Character orbit 2900.c
Rep. character $\chi_{2900}(349,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $9$
Sturm bound $900$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2900.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(900\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2900, [\chi])\).

Total New Old
Modular forms 468 42 426
Cusp forms 432 42 390
Eisenstein series 36 0 36

Trace form

\( 42 q - 46 q^{9} + O(q^{10}) \) \( 42 q - 46 q^{9} + 8 q^{11} - 8 q^{19} - 4 q^{21} + 6 q^{29} + 16 q^{31} + 8 q^{39} - 24 q^{41} - 58 q^{49} - 68 q^{51} + 12 q^{59} - 28 q^{61} + 8 q^{69} + 28 q^{71} + 16 q^{79} + 42 q^{81} - 44 q^{89} - 4 q^{91} - 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2900, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2900.2.c.a 2900.c 5.b $2$ $23.157$ \(\Q(\sqrt{-1}) \) None 116.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+4iq^{7}-6q^{9}-q^{11}+3iq^{13}+\cdots\)
2900.2.c.b 2900.c 5.b $2$ $23.157$ \(\Q(\sqrt{-1}) \) None 116.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{7}-q^{9}-6q^{11}+iq^{13}+\cdots\)
2900.2.c.c 2900.c 5.b $2$ $23.157$ \(\Q(\sqrt{-1}) \) None 116.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}+2q^{9}+3q^{11}+5iq^{13}+\cdots\)
2900.2.c.d 2900.c 5.b $2$ $23.157$ \(\Q(\sqrt{-1}) \) None 580.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}-4q^{11}-3iq^{13}+2iq^{17}+\cdots\)
2900.2.c.e 2900.c 5.b $2$ $23.157$ \(\Q(\sqrt{-1}) \) None 580.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3q^{9}-2q^{11}-iq^{13}+2q^{19}-4iq^{23}+\cdots\)
2900.2.c.f 2900.c 5.b $6$ $23.157$ 6.0.5089536.1 None 580.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{2}+\beta _{4})q^{7}+(-4+\beta _{1}+\cdots)q^{9}+\cdots\)
2900.2.c.g 2900.c 5.b $6$ $23.157$ 6.0.350464.1 None 580.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{5}q^{7}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
2900.2.c.h 2900.c 5.b $10$ $23.157$ 10.0.\(\cdots\).1 None 2900.2.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2900.2.c.i 2900.c 5.b $10$ $23.157$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 2900.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{3}+\beta _{9})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1450, [\chi])\)\(^{\oplus 2}\)