Properties

Label 10.34.a
Level $10$
Weight $34$
Character orbit 10.a
Rep. character $\chi_{10}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
Sturm bound $51$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 34 \)
Character orbit: \([\chi]\) \(=\) 10.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(51\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(10))\).

Total New Old
Modular forms 51 11 40
Cusp forms 47 11 36
Eisenstein series 4 0 4

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

\(2\)\(5\)FrickeDim
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(6\)

Trace form

\( 11 q - 65536 q^{2} + 74568256 q^{3} + 47244640256 q^{4} - 152587890625 q^{5} - 11300222795776 q^{6} + 22560918015772 q^{7} - 281474976710656 q^{8} + 11\!\cdots\!43 q^{9} - 10\!\cdots\!00 q^{10} + 25\!\cdots\!32 q^{11}+ \cdots + 14\!\cdots\!16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
10.34.a.a 10.a 1.a $2$ $68.983$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 10.34.a.a \(131072\) \(-74648412\) \(305175781250\) \(20\!\cdots\!56\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{16}q^{2}+(-37324206-3\beta )q^{3}+\cdots\)
10.34.a.b 10.a 1.a $3$ $68.983$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 10.34.a.b \(-196608\) \(-33025382\) \(-457763671875\) \(39\!\cdots\!66\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{16}q^{2}+(-11008461-\beta _{1})q^{3}+\cdots\)
10.34.a.c 10.a 1.a $3$ $68.983$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 10.34.a.c \(-196608\) \(156523368\) \(457763671875\) \(-86\!\cdots\!84\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{16}q^{2}+(52174456-\beta _{1})q^{3}+2^{32}q^{4}+\cdots\)
10.34.a.d 10.a 1.a $3$ $68.983$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 10.34.a.d \(196608\) \(25718682\) \(-457763671875\) \(-28\!\cdots\!66\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{16}q^{2}+(8572894-\beta _{1})q^{3}+2^{32}q^{4}+\cdots\)

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)